#precalculus | Mathematics | Page 289

echo wagon Apr 17, 2021, 7:19 AM

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It should say something like for all
epsilon > 0

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But if you are doing precalc, the limit definition should be sufficient...

leaden jewel Apr 17, 2021, 7:21 AM

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echo wagon But if you are doing precalc, the limit definition should be sufficient...

If it explains how the function is differentiable at zero

willow bear Apr 17, 2021, 7:21 AM

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not once did i mention epsilon or delta

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(f(x)-f(0))/x has a limit as x goes to zero and that limit is 0

leaden jewel Apr 17, 2021, 7:23 AM

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I don't get it
how do you get that limit for the function bounces from one point to the other

willow bear Apr 17, 2021, 7:23 AM

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you can apply the squeeze theorem

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that's the easiest way to show that this limit exists

leaden jewel Apr 17, 2021, 7:24 AM

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okay i'll see that

noble plume Apr 17, 2021, 5:27 PM

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does anyone know how to do this?

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I know how to do it with just the arcsin, but I'm confused now that arccos was added it

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*in

sick steppe Apr 17, 2021, 5:30 PM

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$\tan(\theta-\varphi)$ and use compound angle

obsidian monolithBOT Apr 17, 2021, 5:30 PM

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moshill1

sick steppe Apr 17, 2021, 5:30 PM

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@noble plume

kindred bluff Apr 17, 2021, 5:30 PM

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With the arccos function, you can refer to that as if it was a cosine function but instead of the angle being the value, you just put the adjacent over the hypotenuse ratio.

noble plume Apr 17, 2021, 5:31 PM

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sick steppe <@!561077787847294976>

I'm kind of confused

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tan(theta - p) and use compound angle?

sick steppe Apr 17, 2021, 5:31 PM

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yes

noble plume Apr 17, 2021, 5:31 PM

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kindred bluff With the arccos function, you can refer to that as if it was a cosine function b...

would the triangle be in quadrant 4

sick steppe Apr 17, 2021, 5:32 PM

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since you can easily find what tan(sin^1(4/5)) and tan(cos^-1(5/13)) is

kindred bluff Apr 17, 2021, 5:32 PM

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It really depends on the angle

noble plume Apr 17, 2021, 5:35 PM

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sick steppe since you can easily find what tan(sin^1(4/5)) and tan(cos^-1(5/13)) is

so am I supposed to find those two separately and subtract??

sick steppe Apr 17, 2021, 5:35 PM

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yes, then use compound angle for tan(A-B)

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$\tan(A-B)=\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}$

obsidian monolithBOT Apr 17, 2021, 5:36 PM

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moshill1

noble plume Apr 17, 2021, 5:38 PM

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sick steppe yes, then use compound angle for tan(A-B)

I'll try it 🙂

leaden jewel Apr 18, 2021, 6:48 AM

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noble plume I'll try it 🙂

If you construct the triangles you'll see that this holds true

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$\arcsin \frac{4}{5}=\arctan \frac{4}{3}$

obsidian monolithBOT Apr 18, 2021, 6:48 AM

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osmium

leaden jewel Apr 18, 2021, 6:49 AM

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$\arccos \frac{5}{13}=\arctan \frac{12}{13}$

obsidian monolithBOT Apr 18, 2021, 6:49 AM

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osmium

leaden jewel Apr 18, 2021, 6:57 AM

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$\arctan(A)-\arctan(B)=\arctan\frac{A-B}{1+AB}$

obsidian monolithBOT Apr 18, 2021, 6:57 AM

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osmium

leaden jewel Apr 18, 2021, 6:59 AM

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then you can apply this formula which you can derive by yourself
and since both the angles lie in first quadrant you can simply plug in the values

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just letting you know this

noble plume Apr 18, 2021, 4:34 PM

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I don't really have a grasp on any of these rip

grave tartan Apr 18, 2021, 7:06 PM

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Draw a diagram for 6

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For 7, Solve for sin(θ) and use double angles

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Split cos^2(2x) into cos(2x)*cos(2x)

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Use half angles

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@noble plume if you don’t know there identities you should learn them

noble plume Apr 18, 2021, 7:25 PM

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grave tartan <@561077787847294976> if you don’t know there identities you should learn them

I solved #7 for now 🙂

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a,b, and c

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trying to do 8 atm

grave tartan Apr 18, 2021, 7:35 PM

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Good work

noble plume Apr 18, 2021, 8:09 PM

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grave tartan Good work

ty 🙂

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I'm sorry for bothering u, but do you have any idea what property I need to look up for #8?

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I've been searching, and still can't find it rip

grave tartan Apr 18, 2021, 8:09 PM

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It’s all good

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Do you know any double angles?

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Double angles are just nice angle sum ones

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Like $\cos^2{2x}$ is just $\cos{2x}\cdot\cos{2x}$

obsidian monolithBOT Apr 18, 2021, 8:11 PM

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AyeWaddup

grave tartan Apr 18, 2021, 8:11 PM

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And $\cos{2x}=\cos{(x+x)}$

obsidian monolithBOT Apr 18, 2021, 8:12 PM

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AyeWaddup

grave tartan Apr 18, 2021, 8:12 PM

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Plug that into the cos sum identity you get $\cos^2(x)-\sin^2(x)$

obsidian monolithBOT Apr 18, 2021, 8:12 PM

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AyeWaddup

grave tartan Apr 18, 2021, 8:13 PM

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Which can also be written as $2\cos^2(x)-1$ or $1-2\sin^2(x)$

obsidian monolithBOT Apr 18, 2021, 8:14 PM

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AyeWaddup

grave tartan Apr 18, 2021, 8:14 PM

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Using the Pythagorean trig identity

noble plume Apr 18, 2021, 8:15 PM

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tysm!

noble plume Apr 18, 2021, 8:24 PM

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grave tartan Using the Pythagorean trig identity

so 2cos^2(x) or 1-2sin^2(x) is the answer?

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isn't the cos supposed to be to the first power

viscid thistle Apr 18, 2021, 9:12 PM

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Yo anyone in here able to help me with a question

dim rampart Apr 18, 2021, 9:34 PM

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If you had posted the question, sure.

pure dragon Apr 18, 2021, 10:34 PM

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hate to ask, but does anyone understand limits with square roots lol?
i can't seem to understand when the sign is supposed to be positive or negative depending on the where the square root is and which infinite its going to

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@here

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Screen_Shot_2021-04-18_at_6.37.43_PM.png

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i believe i can break it down to:
sqrt ( 1 - 0 ) divided by 3 + 0

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but i don't understand how to radical affects the sign of the equation as well as the limit to infinity

bitter nova Apr 18, 2021, 10:41 PM

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for square roots just apply it to the highest term

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so like the top is approximately x^4

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because sqrt(x^8)

pure dragon Apr 18, 2021, 10:42 PM

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sqrt(x^8) = x^4

bitter nova Apr 18, 2021, 10:42 PM

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yea

pure dragon Apr 18, 2021, 10:42 PM

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how come sometimes it becomes like: x^2 = - sqrt (x^4)

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let me see if i can find an example

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Screen_Shot_2021-04-18_at_6.43.18_PM.png

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@bitter nova

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even tho x^5 = sqrt(x^10) --> why does it become negative?? is that because we're finding the limit to negative infinity

bitter nova Apr 18, 2021, 10:45 PM

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that's a really weird way lol

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x^5= - sqrt(x^10) because the square root is always positive

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and a negative to the 5th power is negative, so you add a minus to make the signs the same

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I'd look at it as a minus sign from the x^5 on top, even though that explanation puts it on the bottom

pure dragon Apr 18, 2021, 10:47 PM

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by adding a negative in front of the sqrt, it makes it negative i understand, but ig my question is why am i adding the negative

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because the sqrt is in the denom??

bitter nova Apr 18, 2021, 10:48 PM

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uh it's trying to divide by x^5

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and to convert it to something similar to the bottom you make it like sqrt(x^10)

pure dragon Apr 18, 2021, 10:48 PM

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because they're equal

bitter nova Apr 18, 2021, 10:48 PM

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but x^5 is negative so you add a minus sign

pure dragon Apr 18, 2021, 10:49 PM

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is there a rule as to why x^5 is negative? would x to the power of an even make it positive?

bitter nova Apr 18, 2021, 10:49 PM

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x^5 is negative because it's a limit to negative infinity

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and 5 is odd

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square root is sort of ambiguous because like 2 times 2 equals -2 times -2

pure dragon Apr 18, 2021, 10:50 PM

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then how come in the previous example i posted it was to the negative infinite but i didn't make the sqrt neative

bitter nova Apr 18, 2021, 10:50 PM

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but we chose the sqrt(x) notation to always be positive

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the one before had a 3x^4

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this one is x^5

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like in the end all you need to know is the sign of the final limit

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so like x^5/sqrt(...) is negative for x-> -inf

pure dragon Apr 18, 2021, 10:51 PM

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Screen_Shot_2021-04-18_at_6.51.27_PM.png

bitter nova Apr 18, 2021, 10:51 PM

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and sqrt(...)/3x^4 is positive for x-> -inf

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yea x^5 goes negative for x<0

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x,x^3,x^5,x^7... work like that

pure dragon Apr 18, 2021, 10:53 PM

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thats a pattern i noticed, when x < 0 ... the y was negative

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when the power was odd

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so when the power is odd and i'm going to the negative infinite, then my sqrt will be negative

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right?

bitter nova Apr 18, 2021, 10:55 PM

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no

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the negative came from the x^5

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and it divided it into the fraction

pure dragon Apr 18, 2021, 10:57 PM

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x^13 going to negative infinite would give a negative sign in the fraction because x<0 gives negative values for y

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but if the exponent is even then any value would be positive, keeping the fraction positive

bitter nova Apr 18, 2021, 10:59 PM

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yea

fleet yew Apr 19, 2021, 12:38 AM

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x¹³

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χ¹³

pure dragon Apr 19, 2021, 12:51 AM

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how did u superscript in discord??

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@fleet yew

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lol, just wondering

grave tartan Apr 19, 2021, 1:19 AM

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Specific Keyboard

granite crescent Apr 19, 2021, 2:56 AM

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hi

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um i need help with a question

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so i have to determine the value of x

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for sin 8pi/23 =sinx

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however the catch is that x≠8pi/23

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so idk how to solve that

fleet yew Apr 19, 2021, 5:44 AM

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@pure dragon these are unicode characters

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But my phone keyboard just has them

pure dragon Apr 19, 2021, 10:53 AM

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gotcha

noble plume Apr 19, 2021, 1:14 PM

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does anyone know how to make it so that the cos^2(2x) is written to the 1st power

dark sky Apr 19, 2021, 1:30 PM

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i dont know how to do this

late mica Apr 19, 2021, 1:55 PM

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@noble plume Do you know about power reducing formulas? The power reduction for cos is (1+cos(2x))/2

noble plume Apr 19, 2021, 1:59 PM

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late mica <@!561077787847294976> Do you know about power reducing formulas? The power redu...

yeah, I think I know that, but I can't imply it into the cos^2(2x) 😦

noble plume Apr 19, 2021, 2:02 PM

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late mica <@!561077787847294976> Do you know about power reducing formulas? The power redu...

actually, I didn't know that

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would this just be cos(5.3), or is the angle something different?

late mica Apr 19, 2021, 2:22 PM

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@noble plume I'm not quite sure what that one is asking...It just looks like something that would need to be evaluated, so I'm not really sure. Maybe it's talking about trigonometric form?

noble plume Apr 19, 2021, 2:22 PM

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maybe, I don't know either rip

late mica Apr 19, 2021, 2:36 PM

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@granite crescent This seems like a rotational type of question...For example, say you're solving sin π = sin x, but x can't equal π. If you simply add a full rotation, you're now at 3 π (because a full rotation is 2 π). So, x = 3 π in this case, which would make it at the same angle, but rotationally different so not actually π. Does this help?

viscid thistle Apr 19, 2021, 5:31 PM

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can someone help me convert r=6cos(2θ)sin(2θ) to rectangular form and explain the process?

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i know how to convert polar to rectangular but the 2θ is really getting me

sick steppe Apr 19, 2021, 6:19 PM

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noble plume would this just be cos(5.3), or is the angle something different?

yes 4.1+1.2=5.3

willow bear Apr 19, 2021, 7:07 PM

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no no no moshill don't you know, it's 5.30000000000000004

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(/j)

noble plume Apr 19, 2021, 8:16 PM

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lol

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someone, please help my with 6 and 9

steel venture Apr 19, 2021, 8:24 PM

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for 6 you can use sohcahtoa

noble plume Apr 19, 2021, 8:36 PM

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steel venture for 6 you can use sohcahtoa

could you please elaborate

steel venture Apr 19, 2021, 8:37 PM

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yes

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the arcsin(x/y) means that sin(theta) where theta has sides x and y as opposite and hypotenuse (respectively)

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so in this case

narrow helm Apr 19, 2021, 8:38 PM

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I have a question : how can I find the derivative of the cubic function from the square function ?

steel venture Apr 19, 2021, 8:38 PM

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4 is the side opposite and 5 is the hypotenuse

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so 3 would be the final leg

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and so we have a 345 right triangle

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which have specific angles

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the same idea holds for arccos(5/13)

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so for sohcahtoa we have cah

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so arccos(x/y) yields x as the adjacent and y as the hypotenuse

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so we have a 5 12 13 triangle

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which has specific angles which you can find

jolly raven Apr 19, 2021, 8:40 PM

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?

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@narrow helm like $x^3$?

obsidian monolithBOT Apr 19, 2021, 8:40 PM

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visual of Petter's ascendance

noble plume Apr 19, 2021, 8:43 PM

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steel venture which has specific angles which you can find

ok, I'll try to understasnd what you just said

steel venture Apr 19, 2021, 8:43 PM

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the way i did it feels wrong though

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are you allowed to use a calculator at all?

noble plume Apr 19, 2021, 8:47 PM

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steel venture are you allowed to use a calculator at all?

no, he said no calculator

steel venture Apr 19, 2021, 8:47 PM

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yeah so what i just said probably wont work hold on

noble plume Apr 19, 2021, 8:49 PM

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rip 😭

steel venture Apr 19, 2021, 8:50 PM

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@noble plume ah

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you might be able to use the double angle formula for tan

noble plume Apr 19, 2021, 8:53 PM

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I'm not using a right triangle to solve it if I do that though right

viscid thistle Apr 19, 2021, 9:01 PM

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what is this called in math ? An amount ?${−2≤x≤2,−2≤y≤4}$

obsidian monolithBOT Apr 19, 2021, 9:01 PM

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zeffs

steel venture Apr 19, 2021, 9:05 PM

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noble plume I'm not using a right triangle to solve it if I do that though right

shit you're right

steel venture Apr 19, 2021, 9:05 PM

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obsidian monolith **zeffs**

an interval?

jolly raven Apr 19, 2021, 9:30 PM

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viscid thistle what is this called in math ? An amount ?$\{−2≤x≤2,−2≤y≤4\}$

Inequality?

narrow helm Apr 19, 2021, 10:32 PM

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jolly raven <@403168504267931659> like $x^3$?

Yes

jolly raven Apr 19, 2021, 11:26 PM

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narrow helm Yes

Well you can use the definition of a derivative to find it, $\dv{x} f(x) =\lim_{h\to 0}\frac{f(x+h) - f(x)}{h}$$

obsidian monolithBOT Apr 19, 2021, 11:26 PM

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visual of Petter's ascendance

Well you can use the definition of a derivative to find it, $\dv{x} f(x) =\lim_{h\to 0}\frac{f(x+h) - f(x)}{h}$$
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pure dragon Apr 20, 2021, 12:40 PM

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lim x—>5
((2/x+3)-1/4)/x-5

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I can find it with a calculator easily ig but I wanna know why it equals -1/32

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Algabraically

viscid thistle Apr 20, 2021, 12:45 PM

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yeah so

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have you tried doing anything at all to try to find the answer?

pure dragon Apr 20, 2021, 12:46 PM

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Bunch of stuff that’s wrong I think but yeah

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My scratchpad is messy 😅

viscid thistle Apr 20, 2021, 12:48 PM

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really don't know what you did

pure dragon Apr 20, 2021, 12:48 PM

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Ik

viscid thistle Apr 20, 2021, 12:48 PM

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but do you have any ideas on how you can algebraically manipulate the numerator in any way?

pure dragon Apr 20, 2021, 12:49 PM

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I can’t plug in the limit because it equals out to 0/0

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I mean “direct substitution”

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I’ll use the right terminology

viscid thistle Apr 20, 2021, 12:50 PM

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yeah that's the first thing you usually want try out when encountering a limit.

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but i'm not talking about that

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i'm talking about algebraic manipulation.. are you able to come up with any ideas to algebraically manipulate the numerator?

pure dragon Apr 20, 2021, 12:52 PM

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viscid thistle Apr 20, 2021, 12:53 PM

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,rccw

obsidian monolithBOT Apr 20, 2021, 12:53 PM

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pure dragon Apr 20, 2021, 12:53 PM

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When I multiply 2/x+3, does that multiply the denominator by (x+3) as well?

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Honestly, I think I’m probably going about this the wrong way.

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Bots...

viscid thistle Apr 20, 2021, 12:56 PM

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<@&268886789983436800>

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ty

stuck lark Apr 20, 2021, 12:56 PM

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ty

pure dragon Apr 20, 2021, 12:56 PM

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Ty guys

echo wagon Apr 20, 2021, 12:56 PM

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That was wild

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Almost felt like doing crack

pure dragon Apr 20, 2021, 1:01 PM

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Nvm

viscid thistle Apr 20, 2021, 1:01 PM

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no, you want to make mathematically valid steps, and you can't just multiply $\frac{2}{x+3}-\frac14$ by $x+3$ just because you want to. yes, the idea you had is what we want, to do common denominator, but that is not how we want to do it. instead of pulling out a $(x+3)$ in the numerator out of nowhere, think of multiplying essentially by 1, which is mathematically valid step as you are not changing the value of the expression by multiplying it by 1. Focusing only on the numerator we have: $$\frac{2}{x+3}\cdot \overbrace{\color{green}{\frac44}}^{1}-\frac14\cdot \overbrace{\color{blue}{\frac{x+3}{x+3}}}^{1}$$ and this way you can use $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$ to do common denominator.

pure dragon Apr 20, 2021, 1:01 PM

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2-1 over (x-5)(x+3)(4)

obsidian monolithBOT Apr 20, 2021, 1:02 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:04 PM

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I’ve never really been good at working with fractions like that. Where you have multiple fractions in the same equation

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But thank you for taking the time to explain it to me

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Making the numerator have common denominators makes more sense to me anyways than what my friend tried to explain

viscid thistle Apr 20, 2021, 1:05 PM

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i'm glad to hear

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now, are you able to simplify: $$\frac{2}{x+3}\cdot {\color{green}{\frac44}}-\frac14\cdot {\color{blue}{\frac{x+3}{x+3}}}$$

obsidian monolithBOT Apr 20, 2021, 1:07 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:08 PM

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8/4x+12 — x+3/4x+12

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Now they have common denominators

viscid thistle Apr 20, 2021, 1:09 PM

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good job.

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but use proper parenthesis () to indicate what's the numerator and denominator, like this:
8/( 4x+12***)*** -( x+3***)/(*** 4x+12***)***

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in plain text, \verb|a+b/c| actually implies $a+\frac{b}{c}$ instead of $\frac{a+b}{c}$

obsidian monolithBOT Apr 20, 2021, 1:11 PM

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Al𝟛dium

viscid thistle Apr 20, 2021, 1:12 PM

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and now, try to simplify further from: $$\frac{8}{4x+12}-\frac{x+3}{4x+12}$$ considering once again $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

obsidian monolithBOT Apr 20, 2021, 1:13 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:14 PM

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It’d be (8 - x + 3) / (4x + 12)

viscid thistle Apr 20, 2021, 1:14 PM

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almost.

pure dragon Apr 20, 2021, 1:14 PM

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Would I simplify by plugging in the 5

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5+3 = 8

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8 - 8 / (4(5)) + 12)

viscid thistle Apr 20, 2021, 1:16 PM

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be very careful with the $\color{red}{-}$ in front of the second fraction, this is actually a very common mistake in algebra and you may want to start avoiding it now: $$\frac{8}{4x+12}{\color{red}{-}}\frac{x+3}{4x+12}$$ $$\frac{8{\color{red}{-}}(x+3)}{4x+12}$$

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your mistake was not putting () around x+3, in short.

obsidian monolithBOT Apr 20, 2021, 1:17 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:34 PM

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Now it turns into: (8-(x+3)) ÷ (4x² -8x - 60)

viscid thistle Apr 20, 2021, 1:36 PM

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wait why is it 4x²-8x-60?

pure dragon Apr 20, 2021, 1:38 PM

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Doesn’t this still have the x - 5 underneath it?

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Because we only make the numerators have common denominators

pure dragon Apr 20, 2021, 1:39 PM

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obsidian monolith **Al𝟛dium**

.

viscid thistle Apr 20, 2021, 1:39 PM

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pure dragon Doesn’t this still have the x - 5 underneath it?

yeah we do.

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$\lim_{x\to 5}\frac{\frac{8-(x+3)}{4x-12}}{x-5}$

obsidian monolithBOT Apr 20, 2021, 1:40 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:40 PM

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viscid thistle Apr 20, 2021, 1:40 PM

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pure dragon Because we only make the numerators have common denominators

yeah but the common denominator is 4x-12 not any other

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when writing up the actual steps remember to always add the "lim" part until you've actually evaluated the limit.

viscid thistle Apr 20, 2021, 1:41 PM

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obsidian monolith **Al𝟛dium**

but yeah, this is what we are at right now.

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are you able to simplify 8-(x+3)?

pure dragon Apr 20, 2021, 1:42 PM

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Well the x would be 5, so (5+3) - 8 = 0

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That’s not what it needs to equal

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viscid thistle Apr 20, 2021, 1:45 PM

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ok i see what you're doing, whenever you are doing simplification, usually you want to keep it as (x-5)(4x+12).

pure dragon Apr 20, 2021, 1:45 PM

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ok, so i shouldn't simplify that much

viscid thistle Apr 20, 2021, 1:46 PM

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no, it's about leaving it in the form that is more easily simplifiable.

pure dragon Apr 20, 2021, 1:46 PM

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(8-(x+3))/(5-5)(20+12) -->

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(8-(x+3))/32

viscid thistle Apr 20, 2021, 1:46 PM

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viscid thistle are you able to simplify 8-(x+3)?

can you please answer my questions?

pure dragon Apr 20, 2021, 1:47 PM

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viscid thistle are you able to simplify 8-(x+3)?

it's not +5

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it's 8 - (x+3) with x being 5 which simplifies to zero.

viscid thistle Apr 20, 2021, 1:47 PM

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yeah. +3

pure dragon Apr 20, 2021, 1:47 PM

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8 - (5+3) ==> 0

viscid thistle Apr 20, 2021, 1:47 PM

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don't go too quick.

pure dragon Apr 20, 2021, 1:48 PM

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ok

viscid thistle Apr 20, 2021, 1:48 PM

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simplify isn't plug in 5

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please try simplifying algebraically 8-(x+3)

pure dragon Apr 20, 2021, 1:49 PM

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Ahhhh

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it turns into 8-x+3 because there is a -1 in front of the parenthesis

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i completely forgot about that lol

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is that what you're talking about

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so it's -x +5

viscid thistle Apr 20, 2021, 1:50 PM

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no, be aware of distributing - properly, 8-(x+3)=8-x-3=5-x

viscid thistle Apr 20, 2021, 1:51 PM

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pure dragon so it's -x +5

yeah.

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reminding you what we have right now:

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$\lim_{x\to 5}\frac{\color{green}{-x+5}}{{\color{green}{(x-5)}}(4x+12)}$

pure dragon Apr 20, 2021, 1:52 PM

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(-x+5)/((x-5)(4x+12))

obsidian monolithBOT Apr 20, 2021, 1:52 PM

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Al𝟛dium

pure dragon Apr 20, 2021, 1:52 PM

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idk how to write in the language for the bot

viscid thistle Apr 20, 2021, 1:52 PM

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can you notice something?

pure dragon Apr 20, 2021, 1:53 PM

#

they're going to cancel out aren't they

viscid thistle Apr 20, 2021, 1:53 PM

#

yeah, it will end up cancelling but right now we can't.

#

(-x+5)/(x-5) isn't exactly 1

#

can you algebraically manipulate (-x+5) in a certain way so that we can cancel it with (x-5)?

#

let me emphasise this:

pure dragon Apr 20, 2021, 1:55 PM

#

-1(x-5)

viscid thistle Apr 20, 2021, 1:55 PM

#

oh yeah.

#

good job.

pure dragon Apr 20, 2021, 1:55 PM

#

Whoops, wrong sign

viscid thistle Apr 20, 2021, 1:55 PM

#

are you able now to cancel and plug in 5?

pure dragon Apr 20, 2021, 1:55 PM

#

Yeah, which leaves -1/32. The answer we’re looking for

#

Because 4(5)+12 = 32

viscid thistle Apr 20, 2021, 1:56 PM

#

right.

#

good job.

pure dragon Apr 20, 2021, 1:57 PM

#

Sorry for taking sm time and having you guide me thru it but it really means a lot to me

viscid thistle Apr 20, 2021, 1:57 PM

#

for the record, i'd recommend reviewing algebra specifically fractions/manipulating them, you are going to need them.

#

don't be sorry for taking time, that's totally fine, you're welcome.

noble plume Apr 20, 2021, 3:04 PM

#

#

do I use the power reducing formula for 8?

noble plume Apr 20, 2021, 3:41 PM

#

noble plume

also, I solved #9, but I'm not sure if the sin, cos, and tan are + or -

viscid thistle Apr 20, 2021, 3:41 PM

#

is complex numbers regarding modulus and argument considered precalculus?

stuck lark Apr 20, 2021, 3:53 PM

#

yes

noble plume Apr 20, 2021, 3:55 PM

#

#

These are what I got for 8 and 9

#

I'm not sure if I got either one correct, actually think I got both incorrect

tired star Apr 20, 2021, 8:49 PM

#

hi i really need help i’m failing my math class rn and there’s 3 weeks left of school and i’m a senior and it’s the only thing that’s gonna stop@me from graduating

#

does anyone have a help video or soemthing that can help me with this

#

sick steppe Apr 20, 2021, 8:56 PM

#

Quiz 2 holothink

tired star Apr 20, 2021, 9:00 PM

#

yeah i’m not asking anyone to do it for me i just need a tutorial video or something so i can do it myself

#

if it matters that much i’ll just send a different problem on a hw assignment

lone acorn Apr 21, 2021, 4:22 AM

#

Search up fundamental theorem of calculus formula

#

Is this for 2?

boreal crag Apr 21, 2021, 8:49 AM

#

So for the quotation rule right?

#

in the formula of

Screen_Shot_2021-04-21_at_6.49.26_pm.png

#

Can you use v and u interchangeably

#

forexample for the question such as

#

Screen_Shot_2021-04-21_at_6.50.11_pm.png

#

can x-1 be v as well instead of x+1

#

Wait so in the proof, it was using turning the denominator into v(x)^-1 which means that the denominator must be the v

serene heath Apr 21, 2021, 9:20 AM

#

yes the bottom function is v

muted steeple Apr 21, 2021, 11:59 AM

#

hey, can anyone help me figure out how to get the equation for the parabola from the graph?

willow bear Apr 21, 2021, 12:28 PM

#

can you show the graph?

daring drum Apr 21, 2021, 1:41 PM

#

muted steeple hey, can anyone help me figure out how to get the equation for the parabola from...

I'd use vertex form, y = a(x - h)^2 + k. You know where the vertex is, at the point (h, k). You know where a is positive or negative based on whether the parabola curves upwards or downwards respectively. The only annoying part is figuring out a, which you can do by plugging in x = h+1 (whatever h is). You know which y value this should be equal to from the graph, and you'll get a very nice equation which tells you a in terms of y and k.

#

(then if you need to convert from vertex form back to standard ax^2 + bx + c form, just FOIL (x-h)^2 and simplify)

viscid thistle Apr 21, 2021, 2:57 PM

#

potent drift Apr 21, 2021, 3:46 PM

#

any self-learnining course you know is good? edx, coursera, udemy?

clever pecan Apr 21, 2021, 3:51 PM

#

I personally like coursera

#

it has a lot of free courses

#

(not everything is free though)

#

udemy has more paid courses than coursera, but the quality is good

#

however, I'm not familiar with edx, I'll check it out

#

@potent drift

potent drift Apr 21, 2021, 3:54 PM

#

I have signed up for two in EdX - algebra-like there seem to be more (or at least more structured!) - let me know if you see any interesting @clever pecan pls

#

thx for the suggestion

clever pecan Apr 21, 2021, 3:55 PM

#

np!

#

👍

pure dragon Apr 21, 2021, 4:09 PM

#

#

Do the negative three in the numerator and denominator cancel out first?

#

Plugging in equals zero so direct substitution doesn’t work

#

<@&286206848099549185>

pure dragon Apr 21, 2021, 4:33 PM

#

I need to take the derivative first but can someone explain the how and why?

#

mild swan Apr 21, 2021, 4:46 PM

#

pure dragon I need to take the derivative first but can someone explain the how and why?

you get a 0/0 situation

#

This leads to L'Hopital's Rule

#

Note: when differentiating the numerator, expand the polynomial and use the power rule

#

@pure dragon this help?

sick steppe Apr 21, 2021, 6:00 PM

#

pure dragon

you dont actually need L'hopital like it suggests

solemn flame Apr 21, 2021, 7:22 PM

#

How can I graph this

jolly raven Apr 21, 2021, 7:35 PM

#

First I'd find x intercepts and y intercept

bold fiber Apr 21, 2021, 8:49 PM

#

#

Can anyone help with this please?

#

#

I tried evaluating it and trying to simplify it but its even more complicated, any tips?

mild swan Apr 21, 2021, 9:29 PM

#

not legible unfortunately

bold fiber Apr 21, 2021, 9:47 PM

#

@mild swan it's the limit as x approaches infinity of $$x^2\left(e^{2/x}-e^{2/(x+1)}\right)$$

obsidian monolithBOT Apr 21, 2021, 9:48 PM

#

nas

mild swan Apr 21, 2021, 9:48 PM

#

∞ * 0 situation i see

#

maybe bring the x^2 in the numerator into a 1/x^2 in the denominator and try lhopitals

bold fiber Apr 21, 2021, 9:52 PM

#

mild swan maybe bring the x^2 in the numerator into a 1/x^2 in the denominator and try lho...

that would definitely work, sadly lhopitals is not accepted in our education system

mild swan Apr 21, 2021, 9:53 PM

#

rip

#

hmm

#

can you maybe look at the exponents, create common denominators, and then factor?

bold fiber Apr 21, 2021, 9:58 PM

#

mild swan can you maybe look at the exponents, create common denominators, and then factor...

I didn't really understand your point

mild swan Apr 21, 2021, 9:58 PM

#

if you try to rewrite 2/x and 2/(x+1) so they have the same denominator, then maybe you can factor something out

#

like rewrite 2/x as $\frac{2x+2}{x^2 + x}$

obsidian monolithBOT Apr 21, 2021, 9:58 PM

#

Lighthearted Sand Crab

mild swan Apr 21, 2021, 9:59 PM

#

and like rewrite 2/(x+1) as $\frac{2x}{x^2 + x}$

obsidian monolithBOT Apr 21, 2021, 9:59 PM

#

Lighthearted Sand Crab

mild swan Apr 21, 2021, 9:59 PM

#

Maybe you can factor out an $e^{\frac{1}{x^2+x}}$

obsidian monolithBOT Apr 21, 2021, 9:59 PM

#

Lighthearted Sand Crab

mild swan Apr 21, 2021, 9:59 PM

#

i have no idea

#

lemme try this myself

#

wait, what if you split it up into two limits

#

distribute the x^2

#

not working for me

bold fiber Apr 21, 2021, 10:09 PM

#

Same! this is really confusing

mild swan Apr 21, 2021, 10:10 PM

#

idk which grows/decreases faster: x^2 or e^(1/x)

#

tempted to use lhopitals ~~or desmos~~ bu there's gotta be a way

#

what was the original problem?

#

got a picture?

#

wait nvm lol it was just evaluate the limit

#

were you given any other information?

#

Anyway, the result will definitely be positive since $e^{\frac{1}{x}} > e^{\frac{1}{x+1}}$ as x goes to infinity.

obsidian monolithBOT Apr 21, 2021, 10:11 PM

#

Lighthearted Sand Crab

bold fiber Apr 21, 2021, 10:17 PM

#

from desmos, the limit equals 2 but i can't figure out any way to come up with such result

bold fiber Apr 21, 2021, 10:17 PM

#

mild swan were you given any other information?

not at all

mild swan Apr 21, 2021, 10:17 PM

#

oof

#

probably lhopitals

#

that's the only way i can think of doing this limit

#

try asking in maybe #calculus

past meadow Apr 21, 2021, 11:34 PM

#

double angle formula for sin in reverse

dim rampart Apr 21, 2021, 11:35 PM

#

3sin(10x), you should then get.

tough robin Apr 22, 2021, 12:44 AM

#

what is the square root of -1+\sqrt(3i)

tough robin Apr 22, 2021, 1:03 AM

#

viscid thistle Apr 22, 2021, 1:07 AM

#

tough robin

so there are two ways you could do this:
#1 set sqrt( -1+ sqrt(3)i ) = a+bi, square both sides, match real and imaginary parts to make a system of equations, and solve for a and b
#2 convert -1+sqrt(3)i to polar form, then halve the argument and take the square root of the modulus to get a new number in polar form which you then convert back to rectangular (a+bi) form

past meadow Apr 22, 2021, 1:08 AM

#

ugh thats ugly you'll have to figure out sqrt(3i) in rectangular form first

viscid thistle Apr 22, 2021, 1:08 AM

#

past meadow ugh thats ugly you'll have to figure out sqrt(3i) in rectangular form first

its not that ugly since the angle of -1+sqrt(3)i is pretty nice

past meadow Apr 22, 2021, 1:08 AM

#

sqrt(3i)

#

not sqrt(3)i

viscid thistle Apr 22, 2021, 1:09 AM

#

oh

past meadow Apr 22, 2021, 1:09 AM

#

i was calling the question ugly

viscid thistle Apr 22, 2021, 1:09 AM

#

my bad

#

misread

past meadow Apr 22, 2021, 1:15 AM

#

so yeah the method is to use one of dans methods to get sqrt(3i) then you have sqrt(-1+whatever that is) which you'll have to use one of those methods again to find

rich grotto Apr 22, 2021, 1:22 AM

#

Can someone show how to quadratic equations difference of squares

#

sick steppe Apr 22, 2021, 1:40 AM

#

,rotate

obsidian monolithBOT Apr 22, 2021, 1:40 AM

#

late gull Apr 22, 2021, 6:36 AM

#

guys i need help on a simple problem https://i.gyazo.com/thumb/1200/5dc1f5a8c99ccd716f0878c452d725bf-png.jpg

#

https://i.gyazo.com/thumb/1200/ecc5d034ef2d7399174f7769cea17a24-png.jpg

#

https://i.gyazo.com/thumb/1200/a6ae1c2c5eb77c2ffb733b364016b224-png.jpg

red sky Apr 22, 2021, 6:37 AM

#

I need help on how to graph an ellipse

#

lime sequoia Apr 22, 2021, 6:58 AM

#

@late gull do you know the sum angle formulas?

late gull Apr 22, 2021, 6:59 AM

#

no i forget

viscid thistle Apr 22, 2021, 8:05 AM

#

anyone in here able to help me with a question

willow bear Apr 22, 2021, 8:05 AM

#

http://dontasktoask.com/

Don't ask to ask, just ask

viscid thistle Apr 22, 2021, 8:06 AM

#

willow bear Apr 22, 2021, 8:07 AM

#

okay this algebra so far is correct

#

except, since it looks like you want the \textbf{general} solution, you'll need to write $$3x = \tan^{-1}(2) + k\pi, \quad k \in \bZ$$

viscid thistle Apr 22, 2021, 8:07 AM

#

I dont know how to find all the x's

obsidian monolithBOT Apr 22, 2021, 8:07 AM

#

Ann

viscid thistle Apr 22, 2021, 8:08 AM

#

I understand that

willow bear Apr 22, 2021, 8:09 AM

#

so

#

you have 3x = (number)

#

youre literally 1 step away

viscid thistle Apr 22, 2021, 8:17 AM

#

but there are multiple x's

willow bear Apr 22, 2021, 8:29 AM

#

yes, and?

#

does that somehow create a magical forcefield in front of you that's stopping you from dividing both sides by 3?

steel raft Apr 22, 2021, 2:02 PM

#

#

faint basin Apr 22, 2021, 4:25 PM

#

f(3+x)=(3+x)^2= 9+6x+x^2 f(3)=9 => the limit goes to 0 is (6x+x^2)/x

#

that is 0/0, we can apply l'hopital and we get lim 6+2x/1 which is 6

stray hedge Apr 22, 2021, 4:33 PM

#

guys

#

how would u solve this?

faint basin Apr 22, 2021, 4:38 PM

#

stray hedge how would u solve this?

integration

#

integrating the second derivative will get you the first order derivative and you can find the constant as you have those conditions there

#

after you found the first derivative you integrate again, find the constant and thats ur f(x)

#

integration goes brr

stray hedge Apr 22, 2021, 4:45 PM

#

ahh ok

#

ty

faint basin Apr 22, 2021, 4:48 PM

#

np

echo condor Apr 22, 2021, 8:23 PM

#

#

Screen_Shot_2021-04-22_at_4.07.07_PM.png

#

I have something like this but i feel that tan7theta does not equal y/x because that would be tan theta

serene heath Apr 22, 2021, 9:51 PM

#

try multiplying both sides of that equation by r then converting to cartesian @echo condor

echo condor Apr 22, 2021, 9:51 PM

#

so rtanr=rtan7theta

serene heath Apr 22, 2021, 9:51 PM

#

i meant r=7theta

echo condor Apr 22, 2021, 9:52 PM

#

so then r^2=7rtheta

#

and then x^2+y^2=7rtheta

serene heath Apr 22, 2021, 9:58 PM

#

sorry for some reason i thought that was sin theta on the right there

#

youre kinda almost there youll have sqrt(x^2+y^2) on the left and u know theta is arctan(y/x)+kpi, cuz tan is periodic

echo condor Apr 22, 2021, 10:06 PM

#

serene heath youre kinda almost there youll have sqrt(x^2+y^2) on the left and u know theta i...

yeah but tan7theta cant be y/x cause tantheta is y/x

serene heath Apr 22, 2021, 10:07 PM

#

yes theta is arctan(y/x)

#

so 7theta is 7arctan(y/x)

echo condor Apr 22, 2021, 10:17 PM

#

ohhhhhhh

#

ok thank u so much

quartz inlet Apr 23, 2021, 3:59 AM

#

Given (x-1) (x-3) ^2(x-k) <=0. Find sum of all values of k such that this inequality has exactly 20 integer solutions.
I am getting the answer as 2 but the answer given is 3 . Can someone please tell how to solve this

viscid thistle Apr 23, 2021, 1:16 PM

#

quartz inlet Given (x-1) (x-3) ^2(x-k) <=0. Find sum of all values of k such that this inequa...

was this the original problem?

#

or this

harsh cipher Apr 24, 2021, 6:13 AM

#

#

g(x)= ln(x) increase faster.

#

But I don't know why...

jolly raven Apr 24, 2021, 6:21 AM

#

which base is larger?

harsh cipher Apr 24, 2021, 6:22 AM

#

log(x)

jolly raven Apr 24, 2021, 6:22 AM

#

yep

#

so it takes larger numbers to reach a power of 10

#

10^3 is bigger than e^3

harsh cipher Apr 24, 2021, 6:22 AM

#

if you graph it it's the opposite?

jolly raven Apr 24, 2021, 6:22 AM

#

ln x will grow faster bc it takes quicker to get to 2.5ish than 10

jolly raven Apr 24, 2021, 6:22 AM

#

harsh cipher if you graph it it's the opposite?

?

harsh cipher Apr 24, 2021, 6:23 AM

#

ln(x) increase faster?

jolly raven Apr 24, 2021, 6:23 AM

#

yeah

#

think about it like this

#

e^x grows slower than 10^x right?

#

since e is smaller than 10

harsh cipher Apr 24, 2021, 6:24 AM

#

Yes

jolly raven Apr 24, 2021, 6:24 AM

#

logarithms are inversions of exponential functions

#

so you invert almost everything about the function

#

since first its that e^x is slower

#

and we invert it

#

its now that ln(x) grows quicker

harsh cipher Apr 24, 2021, 6:25 AM

#

Ok maybe I didn't understand over the interval (0,1)

jolly raven Apr 24, 2021, 6:25 AM

#

wait

#

over (0,1) might be a different story then

#

i think the inversion rule really only applies for a positive y

#

but when its negative u itd change

#

ah

#

alright

#

well now we gotta think about it like this

harsh cipher Apr 24, 2021, 6:27 AM

#

okay

jolly raven Apr 24, 2021, 6:27 AM

#

so we said that 10 is bigger than e right?

harsh cipher Apr 24, 2021, 6:27 AM

#

Yes

jolly raven Apr 24, 2021, 6:27 AM

#

but remember than when we have a negative as the expoenent its a fraction

harsh cipher Apr 24, 2021, 6:27 AM

#

Yes

jolly raven Apr 24, 2021, 6:27 AM

#

so taking reciprocals is the same

#

if 10 is bigger than e and we take the reciprocal

#

then 1/10 is smaller than 1/e

harsh cipher Apr 24, 2021, 6:28 AM

#

Ok

jolly raven Apr 24, 2021, 6:28 AM

#

but overall 1/10 is farther from 10 than 1/e is from e

#

so 1/10 would have to grow faster to reach 10 at the same point as 1/e

#

so then log(x) grows quicker over that domain

#

but then for the (1, infty) part u just do the one i talked about earlier

#

so that should be all u need

harsh cipher Apr 24, 2021, 6:30 AM

#

hmmm

#

Okay let me think about this.

lone fulcrum Apr 24, 2021, 6:09 PM

#

15,18,23,26,29,34,37,?,?,?

#

what are the numbers?

#

i was thinking 42,45 48

jolly raven Apr 24, 2021, 9:45 PM

#

I'd look at how the numbers are being added successively

gusty glade Apr 25, 2021, 3:30 AM

#

Does anyone know the best book on Integral calculus?

gusty glade Apr 25, 2021, 3:31 AM

#

lone fulcrum what are the numbers?

42, 47, 52

jolly raven Apr 25, 2021, 3:33 AM

#

gusty glade 42, 47, 52

I'd disagree

#

40, 45, 48

gusty glade Apr 25, 2021, 3:33 AM

#

why?

jolly raven Apr 25, 2021, 3:33 AM

#

+3 +5 +3 pattern

#

Last iteration was the last +3

#

So you would continue from the top

past meadow Apr 25, 2021, 3:34 AM

#

jolly raven +3 +5 +3 pattern

that doesn't work for every term in the sequence

#

23, 26, 29

#

oh i get you

jolly raven Apr 25, 2021, 3:35 AM

#

Yeah

#

+5 +3 +3 is there

#

Bc previous one was 18

gusty glade Apr 25, 2021, 3:37 AM

#

jolly raven +5 +3 +3 is there

hmm ok bro my bad

jolly raven Apr 25, 2021, 3:40 AM

#

gusty glade hmm ok bro my bad

Nah ur good

gusty glade Apr 25, 2021, 3:41 AM

#

jolly raven Nah ur good

actually i thought there was a repetition of 5

#

wrong answer tho

#

i will try to focus on my thinking again

jolly raven Apr 25, 2021, 3:43 AM

#

I mean I make mistakes in math too

#

So it was just a fluke

gusty glade Apr 25, 2021, 4:02 AM

#

no pal actually i felt in confusion
even that was a basic.

fringe raft Apr 25, 2021, 4:20 AM

#

gusty glade Does anyone know the best book on Integral calculus?

Depends on which country and the topics you need

gusty glade Apr 25, 2021, 4:24 AM

#

fringe raft Depends on which country and the topics you need

anywhere and on integration

fringe raft Apr 25, 2021, 4:25 AM

#

Definite integral or indefinite,Are you clear with indefinite ?

gusty glade Apr 25, 2021, 4:31 AM

#

fringe raft Definite integral or indefinite,Are you clear with indefinite ?

both will be good!
is there any book like that?

gusty glade Apr 25, 2021, 4:34 AM

#

fringe raft Definite integral or indefinite,Are you clear with indefinite ?

not pretty good with indefinite

fringe raft Apr 25, 2021, 4:38 AM

#

gusty glade both will be good! is there any book like that?

Joseph edwards integral calculus is a good book which you can try

gusty glade Apr 25, 2021, 4:38 AM

#

fringe raft Joseph edwards integral calculus is a good book which you can try

sure, thanks!

#

A Treatise On The Integral Calculus With Applications, Examples And Problems
Joseph Edwards
this one?

#

@fringe raft

fringe raft Apr 25, 2021, 5:00 AM

#

There’s another book titled integral calculus for beginners you can look into that if you’ve not enough practice

gusty glade Apr 25, 2021, 5:38 AM

#

ok bro thanks!

stone temple Apr 25, 2021, 8:35 AM

#

Hey

#

Not sure is this fits here but

#

Is good understanding of algebra I and some basic trig enough for precalc then calc?

willow bear Apr 25, 2021, 8:35 AM

#

probably.

stone temple Apr 25, 2021, 8:38 AM

#

Okay thanks

muted steeple Apr 25, 2021, 10:53 AM

#

how do i begin solving this?

#

completing the cube :D? cube formula?

#

daheck

echo wagon Apr 25, 2021, 10:55 AM

#

You can use the rational roots theorem to get the roots originally

muted steeple Apr 25, 2021, 10:56 AM

#

i know nothing about that

echo wagon Apr 25, 2021, 10:56 AM

#

But since they give you solutions, you could just plug in to see which ones are solutions

muted steeple Apr 25, 2021, 10:56 AM

#

neither did this course said anything about it.

#

yeah i was thinking the same but then what's the point of this exercise?

echo wagon Apr 25, 2021, 10:56 AM

#

I'm surprised that you would get this question without having done RRT

#

That's the usual way for solving cubics

#

Use RRT to find one rational root, then do long division to get the quadratic factor, then find the solutions of the quadratic

muted steeple Apr 25, 2021, 10:57 AM

#

#

that's how they solved similar one in the notes

echo wagon Apr 25, 2021, 10:58 AM

#

Yes, that's right

#

The rational roots theorem just tells you which numbers to try at the start

muted steeple Apr 25, 2021, 10:58 AM

#

is an advanced concept?

echo wagon Apr 25, 2021, 10:58 AM

#

No

#

Google to see it in action

#

Basically it tells you something about all rational roots of a polynomial

muted steeple Apr 25, 2021, 10:59 AM

#

ok

echo wagon Apr 25, 2021, 11:00 AM

#

So that it limits the numbers you have to check to those that satisfy the condition

#

For all rational roots p/q, p divides the constant term and q divides the leading coefficient

#

So you can just write out the factors of the constant term and leading coeff, and then divide them one by one and test all those numbers.

#

All other rational numbers won't be roots so you don't have to try them

muted steeple Apr 25, 2021, 11:02 AM

#

looking at the wiki atm.

echo wagon Apr 25, 2021, 11:02 AM

#

👍

#

It's probably like the next part in your notes tbh

muted steeple Apr 25, 2021, 11:03 AM

#

#

that's the end

echo wagon Apr 25, 2021, 11:03 AM

#

Oh okay, I guess not

#

That's really wack

muted steeple Apr 25, 2021, 11:04 AM

#

it's an intro course to calculus on coursera

#

it had a lot of good reviews

#

so i decided to try it

echo wagon Apr 25, 2021, 11:04 AM

#

If you don't eliminate any numbers to test, there are infinitely many to try. With RRT, you limit yourself to a finite number of numbers to test

#

What's the course?

muted steeple Apr 25, 2021, 11:05 AM

#

https://www.coursera.org/learn/introduction-to-calculus

Coursera

Introduction to Calculus

Offered by The University of Sydney. The focus and themes of the Introduction to Calculus course address the most important foundations for ... Enroll for free.

#

this one*

#

i really want to get to week 3 with good base understanding.

echo wagon Apr 25, 2021, 11:07 AM

#

I will audit it now to check the content lol

#

I'm sure it's fine

#

Just learn the RRT to help yourself

muted steeple Apr 25, 2021, 11:07 AM

#

a lot of new lingo

#

what is relatively prime?

echo wagon Apr 25, 2021, 11:08 AM

#

Two integers are relatively prime if their gcd is 1

#

It means they don't share any factors except 1 and -1 which are always common factors of any 2 numbers.

muted steeple Apr 25, 2021, 11:08 AM

#

ohh

#

okay

#

am i supposed to understand this ?

echo wagon Apr 25, 2021, 11:10 AM

#

No

muted steeple Apr 25, 2021, 11:11 AM

#

okay so the leading coefficient in my case is not 1.

#

so i need to find factors of p and q that are relatively prime?

#

and that's all the numbers i should be plugging to find the root?

#

oh wow that worked like a charm lmao

#

amazing stuff.

#

thank you.

#

it works for all degrees of polynomials?

echo wagon Apr 25, 2021, 11:22 AM

#

Yep

#

All degrees

#

Ofc there can still be irrational roots (or complex roots), but this will give you all rational roots

woeful island Apr 25, 2021, 6:14 PM

#

Could I check my answer I got for a question here, or should I go to the questions section?

#

(because the question section is pretty packed)

willow bear Apr 25, 2021, 7:25 PM

#

you can post your question & answer to be checked here

#

@woeful island

woeful island Apr 25, 2021, 7:48 PM

#

just #7, had to find the value of K

woeful island Apr 26, 2021, 3:20 AM

#

hmmm

willow bear Apr 26, 2021, 3:37 AM

#

i know i'm several hours late because sleep

#

but the problem statement is incomplete. you want to find the value of k under what conditions?

woeful island Apr 26, 2021, 3:02 PM

#

its ok, i got a friend to help me out lol

daring wolf Apr 28, 2021, 12:00 AM

#

Im so scared to take pre calculus next year

calm vine Apr 28, 2021, 12:05 AM

#

It's not too bad don't worry

loud marsh Apr 28, 2021, 12:33 AM

#

whats the notation for x is the element of all real numbers such that x cannot equal (more than one number)

#

i know for one number it would be

#

{XER|x=/=(whatever number)}

sick steppe Apr 28, 2021, 12:34 AM

#

${x\in\mathbb{R}|x\neq a,b;a\neq b}$

#

that?

loud marsh Apr 28, 2021, 12:34 AM

#

ya but i mean when there is more than one number that x cannot equal

#

like lets say x cant be a or b

#

how do you write that

obsidian monolithBOT Apr 28, 2021, 12:35 AM

#

moshill1

sick steppe Apr 28, 2021, 12:35 AM

#

x cant be a or b, and a and b arent the same

#

ie x cant be 2 distinct values, but can be everything else in R

loud marsh Apr 28, 2021, 12:36 AM

#

okay so what if it was like x cannot equal 1 and 2

#

you dont need to say 1 and 2 arent the same right

sick steppe Apr 28, 2021, 12:36 AM

#

no that's clear

#

so just ignore the 2nd condition of what I wrote

loud marsh Apr 28, 2021, 12:36 AM

#

it would just be {xer|x=/=1,2}?

loud marsh Apr 28, 2021, 12:36 AM

#

sick steppe so just ignore the 2nd condition of what I wrote

okok

sick steppe Apr 28, 2021, 12:36 AM

#

yes

loud marsh Apr 28, 2021, 12:36 AM

#

thanks!

#

im in calc but i forgot this basic part lol

grizzled blade Apr 28, 2021, 1:32 AM

#

hey!

#

im in desperate need

#

#

of help with this question

#

this is a no calculator

#

question

#

for the record

sick steppe Apr 28, 2021, 1:34 AM

#

log_7(2)~.35

#

so you need to find a way to make $\log_7{3}-\log_7{8}$

obsidian monolithBOT Apr 28, 2021, 1:34 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:35 AM

#

yeah

#

i got that far

#

but how do i find the values for those logs?

#

thats what im stuck on

sick steppe Apr 28, 2021, 1:35 AM

#

3=6/2

grizzled blade Apr 28, 2021, 1:35 AM

#

i see

sick steppe Apr 28, 2021, 1:36 AM

#

and you know what log 6 and log 2 are

grizzled blade Apr 28, 2021, 1:36 AM

#

what would log 2 be?

#

0.35?

sick steppe Apr 28, 2021, 1:36 AM

#

1/2 of log 4

#

since $0.5\log_7{4}=\log_7(4^{0.5})$

obsidian monolithBOT Apr 28, 2021, 1:36 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:37 AM

#

fuck thats confusing

#

half of log four would be 1.3/2

#

correct?

sick steppe Apr 28, 2021, 1:37 AM

#

where did you get 1.3?

grizzled blade Apr 28, 2021, 1:38 AM

#

oopd

#

o mean

#

sorry i was looking at the wrong one

#

so log7^3 is 0.45

#

and log 7^8 is

#

1.4?

sick steppe Apr 28, 2021, 1:38 AM

#

grizzled blade so log7^3 is 0.45

?

grizzled blade Apr 28, 2021, 1:38 AM

#

can you go over how to find log7^3 again

#

please

sick steppe Apr 28, 2021, 1:38 AM

#

$\log_7{4}\approx 0.7$

obsidian monolithBOT Apr 28, 2021, 1:38 AM

#

moshill1

sick steppe Apr 28, 2021, 1:38 AM

#

right?

grizzled blade Apr 28, 2021, 1:39 AM

#

how did you get that

#

wait

#

yeah

#

yeah

sick steppe Apr 28, 2021, 1:39 AM

#

reading

grizzled blade Apr 28, 2021, 1:39 AM

#

right

#

sorry

#

super stressed my b

#

so yeah thats right

sick steppe Apr 28, 2021, 1:39 AM

#

so then I can multiply both sides by .5

#

$0.5\log_7{4}\approx 0.35$

obsidian monolithBOT Apr 28, 2021, 1:39 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:39 AM

#

mk

#

so then where does that lead us

sick steppe Apr 28, 2021, 1:39 AM

#

but by log laws, $0.5\log_7{4}=\log_7(4^{0.5})$

obsidian monolithBOT Apr 28, 2021, 1:40 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:40 AM

#

yes

sick steppe Apr 28, 2021, 1:40 AM

#

and square root of 4 is 2

#

so $\log_7{2}\approx 0.35$

obsidian monolithBOT Apr 28, 2021, 1:40 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:40 AM

#

ok pretty simple

#

from there where do we go

#

?

sick steppe Apr 28, 2021, 1:40 AM

#

so you need log_7(8)

#

but 8 = 2^3

#

so multiply both sides by 3

#

$\log_7{8}\approx 1.05$

obsidian monolithBOT Apr 28, 2021, 1:41 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:41 AM

#

whattt

#

how tf

sick steppe Apr 28, 2021, 1:42 AM

#

same logic of multiplying both sides by 0.5

#

cause I can use log laws to get 2^3 inside the log

#

$\log_7{2}\approx 0.35\implies 3\log_7{2}\approx 1.05$

obsidian monolithBOT Apr 28, 2021, 1:42 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:43 AM

#

i see

#

ok that makes sense

#

so how does this help us find the orginial values we need to find

sick steppe Apr 28, 2021, 1:43 AM

#

cause you need log_7(8) and log_7(3)

#

so you found one of them

grizzled blade Apr 28, 2021, 1:44 AM

#

we found log_7(8) correct

sick steppe Apr 28, 2021, 1:44 AM

#

$\log_7{3}=\log_7\left(\frac{6}{2}\right)=\log_7{6}-\log_7{2}\approx .9-.35$

obsidian monolithBOT Apr 28, 2021, 1:44 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:45 AM

#

wouldn't you want to add log7(2?)

#

or multiply

#

to find log7(8)?

sick steppe Apr 28, 2021, 1:45 AM

#

you already have log_7(8)

grizzled blade Apr 28, 2021, 1:46 AM

#

sorry bro this shit

#

is like

#

a forigen language

#

to me

#

its just this one problem on my entire damn worksheet

#

do you think you could write this all down on a piece of paper so i can see your work?

#

its juts so confusing tracking all of this

#

im sorry man

sick steppe Apr 28, 2021, 1:46 AM

#

it's basically how can you make numbers out of 6 4 and 11 given multiplication and division

grizzled blade Apr 28, 2021, 1:47 AM

#

yeah

#

ill try it again

#

thank you for your help

#

i have the answer

#

but

#

im still figuring out

#

how she got it

#

(my teacher)

sick steppe Apr 28, 2021, 1:47 AM

#

yeah no worries

grizzled blade Apr 28, 2021, 1:47 AM

#

im gonna try it again

#

ill lyk if i need help, thank you man

#

hmm so i went and did the entire thing @sick steppe

#

my final answer was -0.35

#

i got log7(3) is 0.7

#

log7(2) is 0.35

sick steppe Apr 28, 2021, 1:53 AM

#

how did you get that?

grizzled blade Apr 28, 2021, 1:54 AM

#

what i did was

#

wait so

#

my value for log 7(8) was 1.05

#

is that correct?

sick steppe Apr 28, 2021, 1:54 AM

#

yes

grizzled blade Apr 28, 2021, 1:54 AM

#

ok so

#

from there

#

i did log7(2) + log 7(3) = 1.05

#

i know the value of log 7^2 is 0.35

sick steppe Apr 28, 2021, 1:55 AM

#

2*3 isnt 8

grizzled blade Apr 28, 2021, 1:55 AM

#

2 to the power of 3

#

is 8

#

so do i multiply by 4 then?

sick steppe Apr 28, 2021, 1:55 AM

#

yeah, so you'd get 3log_7(2)=1.05, which is back where we started

grizzled blade Apr 28, 2021, 1:55 AM

#

ok

#

so from there

#

where do we go

sick steppe Apr 28, 2021, 1:56 AM

#

$\log_7{3}=\log_7{6}-\log_7{2}$ as I previously said

obsidian monolithBOT Apr 28, 2021, 1:56 AM

#

moshill1

sick steppe Apr 28, 2021, 1:56 AM

#

and you know both log 6 and log 2

grizzled blade Apr 28, 2021, 1:56 AM

#

how do we know

#

that equation is true

sick steppe Apr 28, 2021, 1:56 AM

#

cause 6/2=3

grizzled blade Apr 28, 2021, 1:56 AM

#

i see

sick steppe Apr 28, 2021, 1:56 AM

#

and log laws

grizzled blade Apr 28, 2021, 1:57 AM

#

right

#

right

#

yes

#

ok that makes sense

sick steppe Apr 28, 2021, 1:57 AM

#

so $\log_7{3}\approx 0.55$

obsidian monolithBOT Apr 28, 2021, 1:57 AM

#

moshill1

grizzled blade Apr 28, 2021, 1:57 AM

#

ok

#

and we know both from there

#

so the answer is

#

-0.5

sick steppe Apr 28, 2021, 1:57 AM

#

yes

grizzled blade Apr 28, 2021, 1:57 AM

#

alright

#

thank you

#

i think i got most of it down

sick steppe Apr 28, 2021, 1:57 AM

#

,w calculate log_7(3/8)

obsidian monolithBOT Apr 28, 2021, 1:57 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

grizzled blade Apr 28, 2021, 1:58 AM

#

i just get confused witth log rules

#

thank you

#

yo

#

@sick steppe

#

#

could you go through this one with me as well

#

im sorry

sick steppe Apr 28, 2021, 2:03 AM

#

find log 2

#

then log 4

grizzled blade Apr 28, 2021, 2:03 AM

#

alright

#

so i would find log two by

#

dividng log 9^8 by 3?

sick steppe Apr 28, 2021, 2:04 AM

#

yes

grizzled blade Apr 28, 2021, 2:04 AM

#

since 2^3 = 8

#

so log 2 is 0.

#

0.3

sick steppe Apr 28, 2021, 2:04 AM

#

cbrt(8)=2, but yes

grizzled blade Apr 28, 2021, 2:04 AM

#

so log 2 is 0.3

sick steppe Apr 28, 2021, 2:04 AM

#

yes

grizzled blade Apr 28, 2021, 2:04 AM

#

i can square that

#

aka

#

multiply by two

#

for 0.6?

sick steppe Apr 28, 2021, 2:04 AM

#

yes

grizzled blade Apr 28, 2021, 2:04 AM

#

ok yes that worked

sick steppe Apr 28, 2021, 2:04 AM

#

,w calculate log_9(4)

obsidian monolithBOT Apr 28, 2021, 2:04 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

grizzled blade Apr 28, 2021, 2:05 AM

#

thank you

#

@sick steppe hey so

#

i thought i had this one

#

but i was clsoe

#

i don't know where my mistake is so im just gonna tell you what i did

#

first thing i did was find log(3)

#

i got 0.55

#

after that i noticed 2^5 is 32

#

so i went to find log(2)

#

i got 0.35 for log(2)

#

i then multipled that by 5

#

and got 1.75

#

and from there did 1.75 - 0.55

#

and got 1.2

#

but the answer is 1.1

#

@sick steppe you have any idea where i went wrong?

grizzled blade Apr 28, 2021, 2:41 AM

#

,w calculate log_8(2)

obsidian monolithBOT Apr 28, 2021, 2:41 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

grizzled blade Apr 28, 2021, 2:46 AM

#

,w calculate log_8(11)

obsidian monolithBOT Apr 28, 2021, 2:46 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

grizzled blade Apr 28, 2021, 2:46 AM

#

,w calculate log_8(3)

obsidian monolithBOT Apr 28, 2021, 2:46 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

grizzled blade Apr 28, 2021, 2:48 AM

#

,w calculate log_8(2)

obsidian monolithBOT Apr 28, 2021, 2:48 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

viscid thistle Apr 28, 2021, 3:38 AM

#

Is this a place I can find someone to help me understand concepts I am trying to learn in my course?

jolly raven Apr 28, 2021, 5:47 AM

#

It's more like you can ask for homework help.

muted steeple Apr 28, 2021, 10:38 AM

#

can someone explain the highlighted ones?

#

nvm actually figured it out wew

plain turtle Apr 28, 2021, 4:05 PM

#

Determine which quadrant the terminal side would lie given the following information: sin(theta) = -21/29; cot(theta) < 0

#

^ can someone help with this?

#

Would appreciate

somber yew Apr 28, 2021, 4:48 PM

#

@plain turtle What have you thought so far?

vale basin Apr 28, 2021, 5:27 PM

#

https://gyazo.com/d4f8ff762aefa76c8ea68a3ee3a26a0d

Gyazo

#

what is wrong with this solution ?

#

i can't find the problem

willow bear Apr 28, 2021, 6:33 PM

#

i mean...

#

1 + 1/2 + 1/3 + 1/4 + ... is a divergent series

#

that's the issue

#

you're subtracting infinity from infinity

#

and even the alternating harmonic series, ie what you start with, isn't absolutely convergent, so extra care needs to be taken in manipulating those

#

@vale basin

vale basin Apr 28, 2021, 6:45 PM

#

I found the answer already but still thanks 😉

stone vortex Apr 29, 2021, 12:50 AM

#

my class is actually calculus, not precalculus but i feel like this is a pretty basic concept and #calculus is busy lol so..

#

i did a FORTY rectangle approximation and its not close enough to the answer, in the calculator it calculated 7021.7143 for me
is there a better algebraic way to solve this instead of rectangle approximation? i didnt really pay enough attention in class and my finals tomorrow 😬

ebon sorrel Apr 29, 2021, 12:58 AM

#

can you not just

#

$\int_0^4 3x^6 dx$

obsidian monolithBOT Apr 29, 2021, 12:59 AM

#

Wew Lads Tbh

jolly raven Apr 29, 2021, 1:03 AM

#

Yikes

#

Doesn't know integration and has a final

stone vortex Apr 29, 2021, 1:04 AM

#

well another issue there

#

we're not allowed to use calculators, we have to do everything in excel

#

ill figure out how to put it in excel ig

jolly raven Apr 29, 2021, 1:04 AM

#

But integrating it is so easy

stone vortex Apr 29, 2021, 1:05 AM

#

ive prob opened the textbook twice the whole semester tbh i just figured stuff out on trial and error

#

ik its stupid but
im lazy and its been working

jolly raven Apr 29, 2021, 1:05 AM

#

$\int x^n \dd{x} = \frac{x^{n+1}}{n+1}$

obsidian monolithBOT Apr 29, 2021, 1:05 AM

#

visual of Petter's ascendance

jolly raven Apr 29, 2021, 1:06 AM

#

If u have a coefficient before the exponent u just multiply the answer by it since it isn't affected by x

#

@stone vortex so u should just integrate it

sick steppe Apr 29, 2021, 1:18 AM

#

jolly raven $\int x^n \dd{x} = \frac{x^{n+1}}{n+1}$

assuming n!=-1

hasty plinth Apr 29, 2021, 1:42 AM

#

#

Can anyone please help

zealous cosmos Apr 29, 2021, 1:43 AM

#

What does that mean ... "find the symmetry?"

#

Just plug in values for $\theta$

obsidian monolithBOT Apr 29, 2021, 1:44 AM

#

jolimath

zealous cosmos Apr 29, 2021, 1:45 AM

#

Try 0, 90, 180, 270 to start ...

verbal shell Apr 29, 2021, 2:22 AM

#

<@&286206848099549185> this problem was never answered

fringe raft Apr 29, 2021, 3:08 AM

#

verbal shell <@&286206848099549185> this problem was never answered

f” tells us about the concavity of the curve if it’s >0 then it’s concave and if it’s <0 it’s convex. The derivative tells about the slope at a particular point

verbal shell Apr 29, 2021, 3:26 AM

#

fringe raft f” tells us about the concavity of the curve if it’s >0 then it’s concave and i...

wait which one is concave up and concave down

jolly raven Apr 29, 2021, 3:45 AM

#

sick steppe assuming n!=-1

What

fringe raft Apr 29, 2021, 4:09 AM

#

verbal shell wait which one is concave up and concave down

For concave up f” >0

#

Think of it looking at a cup from the top Concave up looks like a cup

blissful peak Apr 29, 2021, 4:16 AM

#

the question is, say there are 5 break out rooms, 4 people per break out rooms, and you have 9 friends. whats the probability of getting into a break out room with one or more of your friends.
i got ~83% and i just want to know if its correct or wrong

hasty plinth Apr 29, 2021, 6:20 AM

#

#

Can anyone please help

#

<@&286206848099549185>

viscid thistle Apr 29, 2021, 8:58 AM

#

blissful peak the question is, say there are 5 break out rooms, 4 people per break out rooms, ...

#

so ~83% would be wrong

#

P(room with one or more of your friends)=1-P(room with none of your friends)

#

each room has 4 people

#

20 people in the class

#

10 non-friends, you, and 9 friends

#

so lets say you're in some room, there will be 3 other people

#

19 choose 3 total ways to choose 3 other people to form the room

#

10 choose 3 ways to choose 3 non-friends so that you end up in a room with none of your friends

#

P(room with none of your friends) =(10C3)/(19C3)

#

P(room with one or more of your friends)= 1-(10C3)/(19C3)

sick steppe Apr 29, 2021, 10:51 AM

#

jolly raven What

If n is -1, the integral doesn't follow reverse power rule

storm plume Apr 29, 2021, 11:02 AM

#

Hey guys, Im a highschool student, and i current am struggling at vector geometry. I was wondering had some recommendations on where i could go to get harder geometry vector geometry?

viscid thistle Apr 29, 2021, 11:03 AM

#

if you are struggling then shouldn't you actually learn the basics ? thonkeyes

storm plume Apr 29, 2021, 11:12 AM

#

i have lern't the basic....i just need to ensure that by doing harder questions i can ensure that i am prepared for everything in the exam

somber yew Apr 29, 2021, 2:11 PM

#

That doesn't sound like an effective learning strategy.

#

Try working out your basics first.

#

If it's a school exam, work through the contents covered in your class through the prescribed textbook.

#

Khan Academy could be a useful supplement.

jolly raven Apr 29, 2021, 4:33 PM

#

sick steppe If n is -1, the integral doesn't follow reverse power rule

I was confused bc I thought u were saying n factorial

sick steppe Apr 29, 2021, 4:33 PM

#

n!=1

jolly raven Apr 29, 2021, 4:33 PM

#

Yeah

sick steppe Apr 29, 2021, 4:33 PM

#

!= means not equal

jolly raven Apr 29, 2021, 4:34 PM

#

I forgot != means not equal to

#

If n=-1 then it's ln(x)

sick steppe Apr 29, 2021, 4:36 PM

#

yes

blissful peak Apr 29, 2021, 5:34 PM

#

viscid thistle

oh yea i get it now thank you

civic sierra Apr 29, 2021, 7:48 PM

#

$\int \frac{2ax+b}{ax^2+bx+c}\dd{x} = \ln{|ax^2+bx+c|} + C$

obsidian monolithBOT Apr 29, 2021, 7:48 PM

#

.itsjustnai

civic sierra Apr 29, 2021, 7:49 PM

#

Is this correct?

#

I assume it is because I've seen it used in a couple of problems, but can someone show me how they got it?

#

nvm i figured it out

viscid thistle Apr 29, 2021, 9:08 PM

#

In vectors, How can directions be in degrees

sick steppe Apr 29, 2021, 9:25 PM

#

viscid thistle In vectors, How can directions be in degrees

cause angles can be measured in degrees

viscid thistle Apr 29, 2021, 9:27 PM

#

sick steppe cause angles can be measured in degrees

so degrees replaces left and right

#

right?

sick steppe Apr 29, 2021, 9:27 PM

#

cartesian vectors can be defined by a distance and a rotation

#

so you rotate however much to look at the destination, then extend there

#

for example if you want the vector [1,1], you rotate 45 degrees CCW from the pos x axis, then extend to be sqrt(2) away

viscid thistle Apr 30, 2021, 2:46 AM

#

How did he get speed?

#

How did he get the dir angle

sly osprey Apr 30, 2021, 3:47 AM

#

pretty easy but idk how to do it

viscid thistle Apr 30, 2021, 5:30 AM

#

relearn what irrationals mean

#

and how to find one between 2 numbers

#

full context of that ?

pseudo furnace Apr 30, 2021, 7:22 AM

#

#

Anyone know how to do these

#

I missed my class today

willow bear Apr 30, 2021, 7:23 AM

#

@pseudo furnace how familiar are you with angle sum, angle difference, and double-angle identities?

pseudo furnace Apr 30, 2021, 7:24 AM

#

Not very

#

It’s a new unit

#

This isn’t even for a grade tho, I just don’t want my teacher to think I’m an idiot lol

#

@willow bear

willow bear Apr 30, 2021, 7:25 AM

#

hrm

#

okay. let's see.

#

since i'd like to know exactly where your knowledge gap lies, here's a simpler question:

#

cos(t) = 0.6 and t is in quadrant 4; find the value of sin(t)

#

would you be able to do this one?

pseudo furnace Apr 30, 2021, 7:27 AM

#

Unfortunately no

willow bear Apr 30, 2021, 7:27 AM

#

mkay

#

okay, are you at least familiar with the pythagorean identity?

#

i.e. sin^2(x) + cos^2(x) = 1

pseudo furnace Apr 30, 2021, 7:28 AM

#

Ya

willow bear Apr 30, 2021, 7:29 AM

#

okay

#

why don't you try applying it to this question i posted then

#

you'll need to learn how to do it in order to tackle the more complicated ones you've posted above.

pseudo furnace Apr 30, 2021, 7:30 AM

#

K

#

Dang it I gotta go, I appreciate the help tho

willow bear Apr 30, 2021, 7:31 AM

#

...welp

pseudo furnace Apr 30, 2021, 7:31 AM

#

Sry:(

willow bear Apr 30, 2021, 7:31 AM

#

i mean, ok, you can look up the relevant trig identities on your own time since i gave you their names

willow bear Apr 30, 2021, 7:31 AM

#

willow bear <@462414436246749184> how familiar are you with angle sum, angle difference, and...

in this message

blazing raven Apr 30, 2021, 10:02 AM

#

Just multiply two arbitrary, length 1 complex numbers.
Real parts a, c are cosine and then b, d are sine.
Ditto for the expression after multiplying.

(a + bi)(c + di) = (ac - bd) + (ad + bc)i
-->
x = (ac - bd)
cos(r + t) = cos(r)cos(t) - sin(r)sin(t)
&
yi = (ad + bc)i
sin(r + t) = cos(r)sin(t) + sin(r)cos(t)

willow bear Apr 30, 2021, 10:03 AM

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i doubt that they're familiar with complex numbers at this point

blazing raven Apr 30, 2021, 10:09 AM

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Eh fair enough.

viscid thistle Apr 30, 2021, 2:15 PM

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yeah no i am not sure where the 43 comes from

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someone else should be able to help

shut shuttle Apr 30, 2021, 2:47 PM

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Is a continuous and decreasing/increasing function f always a bijective function?

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I think it has to be strictly monotonic and then only it can be a bijection

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Can someone confirm?

stuck lark Apr 30, 2021, 3:45 PM

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@shut shuttle don't really need continuous. just strictly monotone is sufficient

shut shuttle Apr 30, 2021, 3:45 PM

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Okay thanks

echo wagon Apr 30, 2021, 4:10 PM

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@shut shuttle when you say a bijection, what are you using as the codomain?

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It's definitely injective

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But it depends on what your codomain is whether it is subjective

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For example, $f: \bR \to \bR, f(x) = e^x$ is strictly increasing but not bijective because the codomain $\bR$ does not equal the range. If you instead made it $\bR \to (0, \infty)$ then it would be bijective.

obsidian monolithBOT Apr 30, 2021, 4:12 PM

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Lunasong the Supergay

muted steeple Apr 30, 2021, 4:12 PM

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Got stuck on this one.

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from my understanding it should be x * ln(6)=x+1

echo wagon Apr 30, 2021, 4:13 PM

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Looks good

muted steeple Apr 30, 2021, 4:13 PM

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no way to isolate x tho?

echo wagon Apr 30, 2021, 4:13 PM

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... Can you isolate x in 2x = x + 1?

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Here 2 is just replaced with ln(6) but you do the same thing

shut shuttle Apr 30, 2021, 4:14 PM

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I don't know what the codomain is, I just know that the range is R and f is a continuous and decreasing function. Can I deduce that f is a bijective function?

echo wagon Apr 30, 2021, 4:14 PM

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You know that the range is R?

shut shuttle Apr 30, 2021, 4:14 PM

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$f: \bR \to \bR$

echo wagon Apr 30, 2021, 4:14 PM

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And by range do you mean image

obsidian monolithBOT Apr 30, 2021, 4:14 PM

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Schrödinger's cat