precalculus

[radiant kite]

what?

yea

the exact answer is 100pi

oh ok

np

what grade are you in

for A i got 1054

then it is 1054.956

i think

not sure

oh

10400.168

try this

1053.757

[slim steppe]

1053.757 should work

[radiant kite]

yea

[viscid thistle]

Anyone up?

[radiant kite]

ya

[noble prawn]

Ye

[flat stratus]

can someone help with this

[willow bear]

do not give out answers.

[viscid thistle]

aight

[flat stratus]

that wasnt the answer but ty

Lol

i asked for help not the answer

[viscid thistle]

do you need help with a specific part of the question or did you just not understand it

[flat stratus]

the question

[viscid thistle]

well, you choose one of the alternatives. supposedly only one of them is correct

it's both a reading comprehension/graph interpretation question
read on the definition of an "increasing", "decreasing" and "constant" function.

[flat stratus]

ok

[viscid thistle]

with the exception of linear functions, any function can have parts where it increases, decreases or stays constant
(linear functions are either increasing, decreasing or constant).

[radiant kite]

b

[viscid thistle]

lmao

[flint bloom]

how can i solve -27x^4 + 18x^3 -48x^2 +15x -18 = 0 for its complex solutions

is there a nice substitution i’m missing or

[uncut mulch]

i suppose you could try factorising

as a product of two quadratics

[flint bloom]

i figured as much but i don’t even know where to start

maybe just suppose two quadratics Ax^2 + Bx + C and Dx^2 + Ex + F and multiply them out and equate coefficients to set up a system

obv this would be the long way bc it’s not at all obvious how i could come up with a product of two quadratics, at least to me

[flint bloom]

for anyone wondering, brute force gave me (9x^2 -3x + 9)(-3x^2 + x -2)

[prisma bridge]

lol u just look at the graph

[radiant kite]

seems about right, but there is an easier solution probably

first factor out the 3

[flint bloom]

of course, i took out a -3 to make the leading coefficients positive

[fair heart]

    -27x^4 + 18x^3 - 48x^2 + 15x - 18
-3 (  9x^4 -  6x^3 + 16x^2 -  5x +  6)

9 = 1 x 9 or 3 x 3
Try
-3 (3x^2 + ax + b) (3x^2 + cx + d)

coefficient of x^3 = -6 -> 3a + 3c = -6
coefficient of x^2 = 16 -> 3b + 3d + ac = 16
coefficient of x = -5   -> ad + bc = -5
constant = 6            -> bd = 6

I am too lazy to solve these, but this is how you would do it by inspection in general. I don't think there's another way to do it.

[flint bloom]

that’s essentially what i did but i didn’t factor out a 3 and made it more difficult for myself

i then made guesses on B and D and subbed them back into everything and checked if i could find a solution

[lucid trench]

heres some cool precalc notes i took #5

[viscid thistle]

What do you use for writing?

[lucid trench]

Pilot precise V5 .5 mm

extra fine

[viscid thistle]

Nice thank you, but this is .5 mm?

[lucid trench]

yes

[tranquil cloak]

Ah, precalc

I love precalc

Favorite math class as of yet

[lucid trench]

AGREED

[viscid thistle]

wait for Real Analysis. lol

[tranquil cloak]

😂

[amber mesa]

Need help with practice exam

Watched yt vids but wasn't helpful

[hasty haven]

hey can someone help me with this problem? I derived that cosx = 1/2 but I think I have to find a sin im not completely sure since I got half credit on the test

[grave yarrow]

if done correctly you should get two solutions for cos

and use your unit circle to find sin value that give you the two angles

if it was cos (something) = [ ( 2 pi ) / 3 ] which is also 120 degrees

the sin value would just be [ ( root 3 ) / 2 ]

[hasty haven]

can you write it out? im ahving trouble following @grave yarrow

[grave yarrow]

i have the answers

idk if i can post it so

[grave yarrow]

is showing the steps okay

[lucid trench]

i think u can but show the steps

ye

[grave yarrow]

k

thx

[grave yarrow]

sin (t) - sin (s) = 2 cos [ ( t + s) / 2 ] sin [ ( t - s ) / 2 ]
2 cos [ (2x) / 2 ] sin { [ ( 2 pi ) / 6 ] / 2 } = 1/2
2 cos (x) sin ( pi / 6 ) = 1/2
Trig Value : sin (pi / 6) = 1/2
2 cos (x) * 1/2 = 1/2
2 cancels : cos (x) = 1/2
Trig Value : cos (pi / 3) = 1/2 & cos [ (5 pi) / 3] = 1/2

if you're finding sin

use unit circle

[wheat oriole]

how do you find the vertical asymtopes for tan functions?

[grave yarrow]

Dividing by zero I guess

Tan x = sin x / cos x

[wheat oriole]

so if i have y=cot(x/2) what would be the va?

[grave yarrow]

The va is always 2 pi n

Increasing by 2 pi

something like this

[hasty haven]

wdym? do I find where sinx = 1/2?

[deep marsh]

um yes

[compact elk]

bruh can some explain me limits and continuity and help me to my sums

iam dying out here

[dry dune]

luv it!

quite curious why the tangent o f the functions aren't included in the diagram?

[simple stratus]

So I'm stuck on promblem one of this review guide I don't understand why cos would be negative
If we are using quadrant 4 of the unit circle .

[simple stratus]

I got this question answered by someone else they said I was right and it was supposed to be cos= positive 4/5
So the teacher probally messed up on the review guide.

[burnt hare]

what an advanced unit circle. should be my new pfp

[amber mesa]

Hi

If anyone could help by displaying the work I'll be very thankful

[flat stratus]

holy what type of math is this 💀

[brisk pasture]

Trig

How would you write f(x)=-4×2^(1-x) in f(x)=ab^x?

[slim steppe]

Basic trig

[dry dune]

i see

[willow bear]

exponent laws

such as: 2^(1-x) = 2^1 * 2^(-x)

and 2^(-x) = 1/2^x...

[gusty pasture]

https://media.discordapp.net/attachments/932296176122859570/1049833663510106172/image.png

y=2sin(x + pi/6)

is this the answer

[gusty pasture]

Actyally

I believe its
y = 2sin(2x+pi/3)

[surreal furnace]

if -sinx(sinx-1)=0 in the interval of [0, 2pi)

shouldn't x= 0, pi, pi/2

[gusty pasture]

got the last one, confused on this

graph is inclusive with it

[gusty pasture]

btw would the shift for the graph be shift to the left by pi/6 and factor by 2? or do i need to add on

<@&286206848099549185> boop

[viscid thistle]

Im doing pre algebra

I dont know this

@gusty pasture

[gusty pasture]

uh ok

Apologies for the ping I got the answer as pi/4

[gusty pasture]

how do i write this as a cosine function

y = 2sin(2x+pi/3)

[gusty pasture]

nvm again

[jovial hound]

When i calculate difference quotient online for ${x}^2+3x+5$, I get $h+2x+3$ along with a graph plot? How is the graph plotted ?

[obsidian monolith]

VECTORFIELDS

[summer ruin]

h = 0

[viscid gulch]

hello

pls

[warped minnow]

∫(f + g) dx = ∫f dx + ∫g dx.

[mild swan]

What have you tried?

[torn dagger]

So if I, for example, do ∫(3x^2 + 2x + 4)dx, I'm very confused about how this translates to being the area under a graph. Can someone explain?

[gusty pasture]

Can someone teach me how to make this all possible values of tan(x)

<@&286206848099549185>

[bitter kayak]

how do you put C and P into a calculator

the green letters just turned all my equations into 0

[minor forge]

All it means is creating infinite number of rectangles under the curve to find the exact area

[shadow bolt]

just open

a

help channel

sal

[viscid thistle]

you want answer in radians or degree? and whats the range?

[gusty pasture]

I already got it but thanks

The questions was vague asf it didn’t give a range

[viscid thistle]

lol

[viscid thistle]

np

[queen pendant]

Hey there, can anyone help me out?

[gritty sage]

same^

[uncut beacon]

i can do one sin but idk what u do when theres 2 and u have to add em

[shut shore]

Evaluate both and then add

[uncut beacon]

oh.

now i feel dumb thats really easy lmao

[shut shore]

🫡

[lucid trench]

heres some cool precalc notes i took #6

[charred blade]

sexy ass notes

i can never take good notes during lectures

if i put more effort into making them look good i cant properly understand what theyre trying to convey

[lucid trench]

luckily my teacher posts the lesson notes after school so i can always check if i miss something

but most of the time the notes i write are while the lesson is happening

holy grail for correction tape btw

[keen parrot]

not to be weird or anything but are you are a girl because I doubt a guy could write notes that neat either way well done

[flint bloom]

is there any way to use the pattern that goes on with the entries to make taking the determinant computationally easier or do you still need to just brute force multiply everything out?

[uncut beacon]

how do you find sin of an angle not on the unit circle? for example; sin(35)

[viscid thistle]

$\sin(35) = \frac{\sin(35 \pi/180)}{\cos(35 \pi/180)}$

[uncut beacon]

can u send image of that in non-text?

[obsidian monolith]

Alois
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[viscid thistle]

bot dead

1sec

[uncut beacon]

can u send image of that in non-text?

o i didnt know if it went through cuz of bot

[viscid thistle]

ye

[uncut beacon]

thx

[viscid thistle]

np

[lucid trench]

i'm a guy

[uncut beacon]

sin(ᵖⁱ⁄₄)cos(ᵖⁱ⁄₁₂) - cos(ᵖⁱ⁄₄)sin(ᵖⁱ⁄₁₂) ?

[willow bear]

this is incorrect

[left karma]

Heya, so does anyone know how the answer for part c was found? I've spent like, an hour just trying to figure it out.

[viscid thistle]

Nah

[willow bear]

well, either i misunderstood you or you said that sin(35°) = sin(35°)/cos(35°)

[rustic forge]

wut?

[lunar quail]

Is this an acceptable answer for proving trig identities? If not, what should the answer look like? I don't need steps, I want to know what the solution SHOULD look like

[summer ruin]

the solution could look like anything

the point of the problem is to show that the equality holds, which it clearly does

[lunar quail]

Thank you

[viscid thistle]

matir

[opal loom]

How do I factor a cubic polynomial with a leading coefficient greater than 1, in less than 2 minutes? Assume grouping doesn't work.

[storm lodge]

cubic formula 😈

or just rrt

[worn agate]

hii

can someone help me with my hw?

thaaank you!

[loud tundra]

Hello, how would you approach this one. Not sure I fully understand the problem

[willow bear]

kirchoff's circuit law

at any node, the total amount entering equals the total amount departing

[long stream]

Help

I need a real life example of the golden ratio

But it has to be something really unexpected since my class and other class can't have the same output

[cosmic girder]

what the fuck

[lucid trench]

that's a really specific application

[vapid plaza]

"application" as if anyone is ever going to use that

[slim steppe]

I'm pretty sure that Iphones use the golden ratio

Or is the Samsung tv

I don't know for sure

[final heath]

Maybe try something to do with the golden triangle. With side lengths 1 and the golden ratio, it has the angles 36° & 72°. Hope this helps

[hushed sphinx]

Does the manufacturing of Vietnamese flags count as a practical application?

(Many other national flags contain stars with the same golden proportions -- e.g. the ones of Ghana, North Korea, Cuba, and USA -- but the star on the Vietnamese one is particularly large relative to the flag itself, so it is easier to notice the proportions there).

[final heath]

I wouldn't see why not

[odd hamlet]

does anyone know how to do #21

[final heath]

A good way to think of it is to find what values of tan (x) could equal √ 3. If that didn't help, then think of values for when sin(x)= √3/2 or when cos(x)=1/2 because tan(x) = sin(x)/cos(x) and (√3/2)/(1/2) = √3

[late nacelle]

help pls

[final heath]

I gotcha

[hushed sphinx]

How did you get the answer attempts in the screenshot?

[final heath]

So first off, we can figure that line A being perpendicular to the ground means that the angle within the triangle must be 180 - angle a in this example

With x now known, we can find the value of what I'll call angle C through 180-A-B

Through this, we can use the law of sine to determine the value of line A with angle C, distance between A and B, and angle B like so

To answer the second question

[hushed sphinx]

(Those numbers 181 and 178 are completely off, but they're roughly in the ballpark of what you'd get if you ignore "NOTE: The picture is NOT drawn to scale", and just measure on the diagram.)

[final heath]

We use our answer to the first question, the distance of line A, to answer the distance between the satellite in the ground at your see in this example

We will draw a 90° from the satellite to the ground, erecting a 90° angle

With this right triangle, we will use the value of A to determine the value of x (seen as the distance between the satellite and the ground), and our good ol trig function cosine seen in this example

Then you'll have both of your answers

I hope this helped you

Crap, the value below x should be A sorry

[hushed sphinx]

It's always good to leave a gotcha for the asker to find, so they get a chance to exercise their own understanding ;-)

[final heath]

Sounds good, I don't usually teach on chat, so I appreciate the pointer

[hushed sphinx]

Tongue somewhat in cheek. But if you want advice, mine would be to try to engage more with the asker, probing what their understanding of the problem is and which parts of it can be salvaged instead of just dumping a clean-sheet roadmap to a solution on them. I appreciate that you're leaving out the actual numbers so you're not actually doing their homework for them. But it's a part of such exercises to give some experience with searching for a workable solution strategy, and just having a route that works handed to them reduces the learning value of that.

[final heath]

Fair enough

I usually do most of if not all of what you've said when I teach in person of course, I'm just totally new to discord teaching if you may. I guess I just thought it would be different. Tbh, with heinsight, it did seem a bit hand holdy and rushed, but I should stick to what I usually do. Thanks for the pointers my guy, every little one counts 👍👍

[late nacelle]

so the distance between the satellitle and station a is 1394.63?

km

[hushed sphinx]

That agrees with my calculator.

(And I did it in a different way than Bagel, viewing the 66 km as something times the difference of two (co)tangents).

(Also, insert expressions of tired outrage at the idea of demanding results with six significant digits, when the angle measurements only had three -- and the difference between those angles which, is what matters most, is only known to two significant digits).

(The right answer in both boxes would be "about 1400 km, give or take a hundred". But the autograder woudn't like that).

[hushed sphinx]

(Also of possible interest: a satellite at that altitude moves across the sky at a speed of at least 0.15° per second when it's near zenith, so one hopes the observers at those two tracking stations have accurate watches to synchronize their measurements by).

[wild ferry]

How would I find the answer to 5b?

[viscid thistle]

seems hard

[fiery bobcat]

Hello guys I just wanted to find out how can I solve vector questions like these ?Im completely confused .

[fiery bobcat]

Yes sir i do know the formula

• operation we using right? I attempted this question 5 times and still got it wrong I dont know why

By adding ax ^2 and ay^2 and getting the sums square root right ?

thank you sir for the guidance ,take your time

no problem

vector v is what?

[obsidian monolith]

ExAllocatePool2

[fiery bobcat]

true

Thank you sir I will apply this to the question then come back to you should I have any difficulties !

[fiery bobcat]

Sir Im still having difficulties

must I send you a picture of my calculations ?

[drowsy shadow]

I need help with this equation I don't understand any of it

[tardy thicket]

Did i do this right?

The box is the solution

[opal tree]

Well your answers, right off the bat, fails to answer the question

Check the intervals

You're missing a couple of solutions

@tardy thicket

What I recommend is just isolating sin^2(x)

[tardy thicket]

what you mean byyy isolating

Sin^2x

[opal tree]

You know what isolate means, right?

Like the dictionary definition

[tardy thicket]

Would I move to the other sir?

Side*

in the beginning?

[opal tree]

$$4\sin^2(x) - 2 = 0$$
$$\implies \sin^2(x) = \frac{1}{2}$$
$$\implies \sin(x) = \pm \frac{1}{\sqrt{2}}$$

[tardy thicket]

Would this be correct

@opal tree

Or keep it as 1/2

[opal tree]

You're missing the -1/2

[obsidian monolith]

Umbraleviathan

[tardy thicket]

Would this be correct

@opal tree

[opal tree]

Yes

,w Solve[{4 Sin[x]^2 - 2 == 0, 0 <= x <= 2 Pi}, x]

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[raven cobalt]

Im exempting from the precal midterm

im chilling this week

only midterms I have is economy, health science theory, photojournalism, and tennis

[tardy thicket]

In the underline part

How did he get ln(1/25)

Curious

@opal tree

If your there or anyone

[ashen skiff]

Logarithm rules

$a*ln(b) = ln(b^a)$

So $-2ln(5)$ becomes $ln(5^{-2})$

[obsidian monolith]

⛄ Is Toast Frosty? ⛄

[opal tree]

$$-2\ln(5) = \ln(5^{-2})$$

[obsidian monolith]

Umbraleviathan

[tardy thicket]

how did they get 1/25?

nvm

it the reciprocal

lmaoo

[peak sinew]

Yep lol

[dusk nova]

someone explain how

[untold ledge]

Let the length be 'l'

Then w= l-3

The use the formula for area of rectangle ie lxb

[inner idol]

(l)(l-3) >= 335

solve the inequality

[untold ledge]

Rip

Lxl-3=335

$l^2-3l=0$

[inner idol]

atleast bro so >=

not =

[untold ledge]

Ok lol

[inner idol]

l^2-3l-335>=0

[untold ledge]

$l^2-3l-335>=0$

[obsidian monolith]

True

[slender lion]

can someone help in #help-9

trust me its precalc

[hallow plover]

can anyone explain to me how to graph logarithmic

[opal veldt]

can somone help me with question 3 part c

[tardy thicket]

cant open it

it weird

[tardy thicket]

you got anyway to show us

in a different photo

[rich elbow]

change it into exponential form

then plug numbers into x and solve for y to get points

[tepid yew]

Can someone help me with this, its an optimization problem

[summer ruin]

draw the picture of what the problem is describing

[long stream]

Guys

I need 3 vertical stretching examples with solutions

To pass for my project in the morning

I also have like 8 more different 3 examples needed

But I need vertical stretching

Since I have no idea what that is

[final estuary]

Im struggling with finding the period and building a function for this graph

[rancid viper]

You mean like to find what is the period pf the red wave?

[lucid trench]

The period is 2pi/frequency

Essentially, I'm asking you what 2pi divided by what will get you 60?

[viscid thistle]

Can Someone Help with This?

Please… @lucid trench @rancid viper

[hushed sphinx]

Don't ping random users for help.

[viscid thistle]

Oh, Sorry

Can you Help Though?

[viscid thistle]

Please, Will Someone Help Me?

[lament tendon]

Lol

Why don't you open a thread about it

[flat stratus]

Help

[drifting parrot]

D?

[late sable]

Please help 😭

[drowsy granite]

if F' is the derivative then it's at 0

[late sable]

So I have been trying to solve this and based on my understanding the answers are all wrong. I solved it first on the basis that they want the 2nd derivative but that's not one of the answers. Then I tried to find the derivate and replace the t with (2). That also is not in the answers. Am I being stupid or are the answers wrong?

[cloud dagger]

can i see ur work?

[late sable]

Aight just a sec

Actually nevermind. I got it now. It's 8

[viscid thistle]

How? @viscid thistle

[frank acorn]

Does anyone know vectors here?

The angle between a and b is 60 and a I have to calculate that cross product

I don't know if what I did is correct or not

[proud basin]

I'm confused on this

[viscid thistle]

Can someone explain to me why |x| isn’t differentiable at 0? Aren’t the one sided limits the same, and isn’t it defined at 0 to? Therefore, the function is continuous, but not differentiable at 0 apparently? Can someone explain to my why it isn’t differentiable mathematically if in fact it is continuous? I understand graphically that there can not be a tangent line on a vertex, however mathematically I don’t understand.

[sturdy olive]

The slope from the left is -1, slope from right is +1

A derivative is found by basically inching closer and closer together to a point, but at x = 0 on y = |x|, there is no gradual change in slope, it goes straight from the slope being -1 to +1

[summer ruin]

already answered in #calculus

[sturdy olive]

I’ve got a question myself now;
would y = (-2)^x be considered an exponential function?

I know the variable is the exponent, but it isn’t an actual function due to the base being negative, right?

[viscid thistle]

The base must be greater than 0 for it to be a exponential function.

[odd abyss]

what does one value of x mean

the absolute value of x?

cause the negative answer is -3/2

but they only want 1

[uncut mulch]

there are two solutions to that quadratic,
they just want you to submit one of them

that's what they mean by "one"

[burnt hare]

😭

[viscid thistle]

did x = 0 work?

[unreal folio]

sup, do you still need help?

[viscid thistle]

lim is for limit, and x with the arrow, when x approches -1 right?

[summer ruin]

these are all specifically approaching -1 from the right

[viscid thistle]

ok alright thanks

[jolly tinsel]

(2x + 3)^2 - 6x - 9 = 0
(2x + 3)^2 = 6x + 9
(2x + 3)(2x + 3 ) = 3(2x+ 3)
D.B.S by 2x + 3
2x + 3 = 3
2x = 0
x = 0

[summer ruin]

good ol' division by zero

[sullen saddle]

i was wondering what do u call this maths for advance study

[summer ruin]

calculus

[split fractal]

how to solve this?

[viscid thistle]

calculus with limits

[vital swan]

how's trigonometry?

I'm taking it second semester in high school and just got done with college algebra.

[viscid thistle]

depends on the person

[opal tree]

Precalculus, it seems

[opal tree]

Understand your geometry and ratios and it's a cakewalk

[opal tree]

Just subtract 2Pi until you can't anymore

Coterminal angles always have a difference of 2πn, where n is an integer

[viscid thistle]

Can anyone help me with this

How is tan inverse of an odd number =π/2

[summer ruin]

this has nothing to do with numbers being odd

the limit arctan(n) as n approaches positive infinity is pi/2

[viscid thistle]

the inverse of an odd function is odd. But here it just asks what value of t satisfies the equality tan(t) = 1.

that's all an inverse function is:
\begin{align}
tan(t) = 1 \
tan^{-1}[ tan(t) ] = tan^{-1}( 1 ) \
tan^{-1}[ tan(t) ] = tan^{-1}( 1 ) \
t = tan^{-1}(1) \
\end{align}

oh

[obsidian monolith]

roland202

[viscid thistle]

oh you weren't asking that i'm drunk

[viscid thistle]

well, f(t) = tan(t) is an odd function. So for it to have an inverse, you restrict the domain to the vertical asymptotes to the right, and left of the origin

[viscid thistle]

someone pls help im so lost

i need to find H

[storm lodge]

$(\text{cotan} 12^\circ+\text{cotan}33^\circ)\cdot{h}$

bruh

[viscid thistle]

huh lol

wait write in mathway and send pic

[obsidian monolith]

BuboBlakistoni

[storm lodge]

here

[viscid thistle]

oh ok

wait but how

[storm lodge]

because you find the bases of the two triangles

cause its split at the bottom

[viscid thistle]

yes

[storm lodge]

then just sin cos stuff

[viscid thistle]

but since anhles arent same the base isnt gonna j be 50-50

[storm lodge]

ik

so we find each of them

seperately

then add them

[viscid thistle]

how

[storm lodge]

take the left triangle

and the right triangle

find the base of those

then add the two bases

[viscid thistle]

how do i find the base tho 😅

[storm lodge]

do you know trig

[viscid thistle]

yes

oh wait

im a dumbass

[storm lodge]

use trig functions

haha

[storm lodge]

its this

once you do the trig

[viscid thistle]

wait wouldnt that turn into tan(12)=h/x

[obsidian monolith]

Kirra

[viscid thistle]

thats cool lmao

[storm lodge]

wdym by x

the first base?

yes

then same for the second base

[viscid thistle]

how do i differentiate #5 from first principles?

[blazing parrot]

I got a final tmr right. Could someone show me how I would graph y=cscx

[sturdy olive]

Did I do c. and d. Right?

[slim ingot]

I’m confused

[tardy thicket]

in the blue did I do this step correctly

also here the question “simplify as much as possible. Use special products whenever possible”

[tardy thicket]

stuck on this problem and unsure how to solve it

[viscid thistle]

Thanks 👍🏻

[patent vortex]

@tardy thicket in the numerator, if you square a sqrt, the sqrt cancels out and in the denominator you have two t√(1 + t) so you can simplify that too

[hazy hollow]

oh i got that a while ago my b

you were right tho

[oblique gazelle]

Can someone help me understand how the author simplified the expression as shown?

[summer ruin]

factored out (n+1)!

then (n+1)! * (n+2) = (n+2)!

[oblique gazelle]

Ah, ok

[river hound]

anyone pls tell me how do i get started with calculus

and what all should i know for it

i am in grade 9

pls respond

[viscid thistle]

calculus follows directly after learning functions.
you need to be proficient in dealing with polynomial, trigonometric, rational, logarithmic, exponential, and absolute value functions.

this includes concepts like domain and range, asymptotes, max/min, roots, etc. you should be familiar with the fundamental theorem of algebra and the remainder theorem.

[viscid thistle]

do this:
https://www.khanacademy.org/math/precalculus

(skip matrices, vectors, conic sections, and complex numbers. you usually pick it up later)

[river hound]

thanks

[short saddle]

i don't know where to start with this problem

[patent vortex]

i would start with

x = a + 1/a, y = b + 1/b, z = c + 1/c

so f(x,y,z) = 0 and abc = 1

[frozen plume]

I need trig help.

Anyone know how to solve this? I created an equation that’s close, but something is just slightly off. I would appreciate any help

[tired geode]

I HATE PROOFS

With a passion

[steady birch]

your min has to be at dec 21st and max at jun 21st, did you apply a phase shift?

(assuming northern hemisphere, otherwise its the other way around)

[frozen plume]

This is what I made

Underneath pi should be 182 not 184

@steady birch

[steady birch]

why is it pi/182 and not 2pi/365?

the 3.7 magnitude is find and the 12 vertical shift is also correct

(idk why you chose a -3.7 it just overcomplicates things)

"cos" is also okay it works just the same as "sin" so i wouldnt change that

Now you have $D(t)=3.7\cos\left(b\cdot t-\text{Phase Shift}\right)+12$

[obsidian monolith]

Fang

[steady birch]

do you know how to solve for phase shift @frozen plume ?

[frozen plume]

I don’t know what phase shift is

Is the just horizontal shift

[steady birch]

yes

[frozen plume]

I know cos - cos sin -sin are all the same I was just trying to line it up with the graph

At t=1

[steady birch]

"phase" instead of horizontal is usually how you refer to it with trig functions because it corresponds to an angular shift in the function

or at least thats how i think about it

[frozen plume]

I did pi/182 cuz it’s half of 364, Jan 1st is t=1 so 365-1 = 364 2pi/364=pi/182

[frozen plume]

Ok thanks

[steady birch]

for the B coefficient of t in the function you should go by 2pi/period

dont go by the indexing of days that will just get confusing

[frozen plume]

This is the closest I can get to having the values lining up

[frozen plume]

well the period would be 1 year? Right?

[steady birch]

yes 1 year is 365 days

why are you still estimating with desmos 😭

use 3.7cos(bt-C)+12

you already have b

[frozen plume]

This is the goofiest problem ever

I swear I’m not this dumb btw I got an 100 on my graphing trig functions test yesterday

How would I solve for phase shift

I was using 355 days as the minimum to make it a -cos function

And then using the distance from 355 to 365, so +10 as the phase shift

[steady birch]

info you have:
values from 8.3 to 15.7 --> (15.7-8.3)/2=3.7 amplitude, (15.7+8.3)/2=12 vertical shift

period of 365 --> B=2pi/365

min at 355, max at 172

we are using positive cosine so a phase shift correlates to shifting the peak (max at 172) --> 172=C/B where D(t)=3.7cos(Bt-C)+12

172=C/(2pi/365) --> C=344pi/365

--> D(t)=3.7cos((2pi/365)*t-344pi/365)+12

when it all comes together

[frozen plume]

YO YOU GOT IT

[steady birch]

you could have used -cos if you did the phase shift with respect to the minimum

[frozen plume]

WITHIN .5

[steady birch]

or sin if you shifted it to halfway between the two solstices

[frozen plume]

i love you

Ok

Yeah that makes sense

[steady birch]

(the 0.5 error comes in because of the day indexing)

[frozen plume]

Wdym indexing

[steady birch]

like each day is numbered

[frozen plume]

Oh yeah

[steady birch]

sorry i use indexing in cs a lot lol

[frozen plume]

Cs?

I dont knkw the terms lmao

It’s fine

[steady birch]

not math

[frozen plume]

Thank you for the help I really appreciate it

[steady birch]

make sure this process makes sense

it is much better and more time efficient than graphically guessing

[frozen plume]

I just gotta look at how you got the c value

Nah for sure

We were only supposed to graph certain priblems

I was using a graphing calc to check my graph

[steady birch]

https://www.varsitytutors.com/precalculus-help/find-the-phase-shift-of-a-sine-or-cosine-function

this has a simple explanation for an example problem

[frozen plume]

Bruh thank you so much

Genuinely

[steady birch]

np

seeing the desmos guesses =

[frozen plume]

Yo I’m actually so slow

We did the phase shift thing in class

J just realized there has to be two sets of parenthesis

[steady birch]

sometimes you have to get stuck on a problem to realize how useful some things are

fully reasonable

[frozen plume]

Like I was putting everything into one equation but if I wrote it down with the period outside another parenthesis it would’ve worked

[grave valve]

Okay s like if i know the function is increasing from -7 to -5 and then at -1 to 7, Would I write it as f(x) is increasing on the interval "[-7,-5]U[-1,7]" or "(-7,-5)U(-1,7)"

I'm leaning towards the second option but like grr it's a simple writing mistake that will cost me a bunch

[summer ruin]

is it defined on -7, -5, -1 and 7?

[grave valve]

Yeah

That's the graph of the derivative

[summer ruin]

if the exercise specifies to determine strict inequality f'(x) < (>) 0 then you use strict brackets

otherwise it doesn't matter as long as your intervals contain no common point

[grave valve]

Wait yeah I got it alr

[grave valve]

This part here

Thankksss

[short saddle]

where to go afterward

@patent vortex

[steady birch]

in this case, i would assume that your professor/teacher is looking for "f(x) is increasing on the interval [-7,-5)U(-1,5)U(5,7]" because when f'(x)=0 (at those excluded points), then it is not increasing

where "[]" is inclusive and "()" is exclusive

i would argue that it does matter separately from the common point issue

[keen pike]

can someone help me?

[jovial thorn]

[keen pike]

I basically missed a unit for composition of functions etc and we have a test today, I am willing to pay if someone can help me out@

[grave valve]

Yeah alr I figured that out tyyy for confirming ❤️ ❤️ ❤️

[willow bear]

we do not offer cheating on tests or exams

[hushed sphinx]

A function is not increasing at a single point -- that's a property the function can have over an interval. This can be satisfied even if the derivative is 0 at some points in the interval. The standard example is x³, which is increasing on all of R even though its derivative is 0 at x=0. And @grave valve's function is shaped essentially like the bend of x³ near x=5. It is increasing on all of [-1, 7].

[steady birch]

That seems poorly defined to me… i would expect x^3 to be non-decreasing on all of R but not strictly increasing on all of R i would expect (-infty, 0)u(0,infty) as a union of open intervals… do you have somewhere i could read about that more? I understand a function is not increasing at a point but points can be excluded from intervals, no?

[hushed sphinx]

The defintion of "f is strictly increasing on D" is that f(a) < f(b) whenever a,b in D with a<b.
So if you want to claim that x³ is not strictly increasing on R, you need to be able to show a pair of a and b such that a < b, yet not a³ < b³. Can you do that?

[steady birch]

Ah ok i see

That does make a lot of sense

[turbid oxide]

How did they determine those were the zeroes and poles

They skipped a step where they factored the numerator and denominator

[willow bear]

well factor they did

really just guessing one nice factor is enough to factor the cubic on the top - and the bottom has s as an obvious one and another lucky guess will get you your factorization

[worldly grail]

https://cdn.discordapp.com/attachments/486841106298961930/1056273202738892930/image.png

Im guessing i have to take limits -1/2 and 2 but

what equations should i take

[summer ruin]

don't cross post

[viscid thistle]

How can I find 19 and 23 algebraically without having to look at its graph?

This, doesn't make sense to me, I was simply tipping in numbers into my calculator and looking at the graph. Otherwise, I wouldn't just left the answer as 7 & 11

[hushed sphinx]

(pi/6)·12 = 2pi, so the period of the function is 12.

Adding 12 to each of 7 and 11 gives 19 and 23.

(The actual period of lunar tides is about 12h25m, not 12h, but the model in the exercise seems to ignore that).

[viscid thistle]

Ooh okay, I get what you mean, know that I recall, I have done a similar problem like this, where I had to keep adding 2pi, to get all the solutions in a 0 to *#*pi interval. Thank you troposphere!

[warm shell]

Uhh π-π/6= 5 π/6 right?

[formal cliff]

Why are we applying the LAPTU rule when there is no 1x^2 polynomial function in this question?

Friends, can you look at this question and help?

[vapid plaza]

Bro this is #precalculus

[viscid thistle]

Oh whoops! I'll correct that negative to a positive sign, thank you!

[plain sable]

Hey can we say the for every differentiable function f(x), f’(x) is continuous?

[hushed sphinx]

You can say it, but it wouldn't be true. :-)

The standard counterexample is $$ f(x) = \begin{cases} 0 & \text{when }x=0 \ x^2\sin(1/x) & \text{otherwise} \end{cases} $$

[obsidian monolith]

Troposphere

[hushed sphinx]

(and this is not in any reasonable sense PREcalculus ...)

[plain sable]

Ohh okay..I was confused why this happens though cuz I thought if a function is differentiable then the f’(x) should be continuous…

Should I ask this in calculus Chanel?

[hushed sphinx]

That would be a better place for follow-up discussion, yes.

[plain sable]

Kk

[hazy hollow]

need the blanks

[mild swan]

What have you tried?

[willow bear]

do not give out answers

[fervent wyvern]

csc(B) is 1/sin(B)

[fervent wyvern]

sin(B) is b/c

[jagged nacelle]

Is precalc much harder than algebra 2?

[sturdy grotto]

May I know how to find the derivative of f(z) = Im z?

[sturdy grotto]

Not sure how to just get the imaginary part, but i know the form is x+iy

[willow bear]

this function is not differentiable @sturdy grotto

[sturdy grotto]

Yea, I just found out using Cauchy Riemann

Anyway, thanks

[viscid thistle]

I have to prove with the epsilon-delta-criteria that the function $f(x)=\frac{1}{x^2-x-2}$ is continuous in the interval (0,1). This is how far I got $\ f(x)-f(\hat{x})=\frac{1}{x^2-x-2}-\frac{1}{\hat{x}^2-\hat{x}-2}=\frac{\hat{x}^2-\hat{x}-x^2+x}{(x^2-x-2)(\hat{x}^2-\hat{x}-2)}$ But what do i do now?

[obsidian monolith]

Plazzi

[viscid thistle]

this doesn't help me at all

Is this even precalc?

[stable dust]

1+1

[viscid thistle]

= 3

[fast oxide]

if they ask for the area do i answer -6 area units?

but area cant be negative

[mild swan]

The area of the region is equal to 6 square units correct

But in terms of integrals (that is how we define area for integrals), it can be negative

Area under the x-axis is negative, and area above the x-axis is positive.*

*In the context of integrals

This may also be better fit for #calculus

[fast oxide]

oh yeah my bad

thank you a lot tho

[viscid thistle]

no what 1 + 1? bruh here is my work to prove it is 2

[viscid thistle]

ohh ok

thanks

i understand why now

good

[warm delta]

bro precal is easy

[lucid trench]

first you have to determine if 11pi/9 is within the domain of the inner function (tan). after that, you evaluate tan(11pi/9), then figure out if that value is within the range of tan^-1 (which is all real numbers)

[lucid trench]

heres some cool precalc notes i took #7

[viscid thistle]

I'm looking at transposing formulas right now. I don't know how to start or where. I'm tempted to grab a ruler but I doubt that's what my teacher intended. 🤣

[summer ruin]

use the information it provides

[viscid thistle]

By the looks of it W should = 2a, 1.5a or somewhere in between. But the question says nothing about estimating, so I don't want to go with that.

[summer ruin]

each window is h meters high and w meters wide

the question does not ask you to represent h or w in terms of a and b or vice versa

[viscid thistle]

I'm still a little bit lost. I'll just write some stuff down and see where my train of thought goes. Thank you for pointing me in the right direction.

[viscid thistle]

ok

[viscid thistle]

wow very cool and organized. I see a little frog there too hehehe

and very good hand writting

[lucid trench]

heh yeah thank you so much

[zinc fulcrum]

whattt

[slim steppe]

Care to elaborate further?

and clearer

[vagrant kestrel]

can anyone help me with a question, its on equations of tangents and normals

[zinc fulcrum]

someone probably can, just ask 🙂

[vagrant kestrel]

i dont know if this belongs in the pre calculus section

wait nevermind ignore that, i sent the wrong question

aaa

[zinc fulcrum]

i*sqrt(6*4) and i*sqrt(4*6) are the same, what’s the issue?

sqrt(6*4) and sqrt(6)*sqrt(2) are not the same, to point out one problem

[slim steppe]

You extract the greatest perfect square

(4)

Hence 2i radical 6

[true cedar]

is it possible for someone to rate precalculus by blitzer textbook? is it gonna give a strong foundation on all the topics before calculus? i wanna know since its 1400 pages long and i don't wanna dedicate my time to something bad

[summer ruin]

I wouldn't trust a math book that features this many pictures

but there's only so few things to learn in the precalculus, you're not going to find a book that has vastly different content

[young spire]

hey guys do yall have a calculus channel

for the 12 graders

[viscid thistle]

#calculus

@young spire

[boreal cave]

Jesus christ where would you need so many trig identities

[neon tartan]

Pretty Neat Notes unlike mine.

[neon tartan]

Half angle formula other variations

[dark aurora]

Hell

[boreal cave]

Not wrong lol

Fuck "pre calculus"

I've gone up till calculus 3 and never needed this shit lol

[viscid thistle]

bruh, pre-calc is so easy

[viscid thistle]

17.89

[boreal cave]

"Pre calculus" isn't necessary if you already have a strong mathematical background before learning calculus

Learning all these things seems like overkill considering it's unlikely if we'll ever use them

Instead you should learn about complex numbers, vectors, and matrices

Something like that would be more useful

[hushed sphinx]

That sounds a lot like "it isn't necessary to learn such-and-such if you already know it".

[frank vine]

Ok i might h ave derived another identity

I want to ask if its correct

[obsidian monolith]

Jagteshwar(JPS838898)

[willow bear]

you know you can throw these into WA and check for yourself, right...?

but also this looks a little suspicious

also bad tex, somehow. what's with that eight

,w sin(4x) = |cos(x)| (4 sin(x) - 8 sin^3(x) )

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Ann#0413

[willow bear]

well, it appears your identity is incorrect.

@frank vine

[frank vine]

Huh

I replaced cos with the sqroot

So instead of abs value it should just be cos a in graph

Then should work I think

Yeah seems to work

[willow bear]

cos(x) ≠ sqrt(1-sin^2(x)) generally

[frank vine]

Hmm I’ll def verify with Desmos next time

[frank vine]

Is that because of the 4 quadrants and the functions type (even/odd)?

[solar olive]

shouldnt it be sign(x) sqrt(1 - sin(x)^2)

[frank vine]

Like how cos is always positive but sin is negative from pi to two pi

Wdym?

Doesn’t work

Eh

[willow bear]

it's simpler than that tbh

sqrt(x^2) = |x|, not x

[torn sluice]

how to write

sec inverse

on calculator

[golden gate]

@torn sluice isn't sec inverse cos?

[willow bear]

@torn sluice arcsec(x) = arccos(1/x)

[keen lichen]

hello

what is a value of a definite integral of a constant

[opal tree]

Like the significance of $\int_a^b Cdx$?

[obsidian monolith]

Umbraleviathan

[keen lichen]

yes

[opal tree]

Area of a rectangle whose base length is b-a, height is C

I mean that's just geometry

[keen lichen]

so it's just b - a ?

[opal tree]

No

[opal tree]

_ _

The integral can be described as the area between a curve and the x axis

[keen lichen]

no i mean, what's the exact value then

[opal tree]

_ _

[keen lichen]

of this expression

[keen lichen]

ok

[willow bear]

@hazy hollow do you still need help with this?

[frank vine]

So i want to confirm this but i think i have derived the formula to obtain sin (nx) purely in terms of the powers of sin x and i obtained this

Thats is according to desmos equal to sin nx

And then i tried same for cos nx

And got this

And same according to desmos this is true

But just want to know if others get same answer

As there isant any convinient way i could plug into wolfram

[frank vine]

I worked from the demoivre’s theorem

That was starting point

Then ended with these

[willow bear]

show your calculation

[hazy hollow]

Yes

[willow bear]

okay. was the a = 16.583 value written by you?

[hazy hollow]

Yes

And the software says it’s correct

[willow bear]

,calc sqrt(18^2 - 7^2)

[obsidian monolith]

Result:

16.583123951777

[willow bear]

okay yeah checks out

do you know the SOH-CAH-TOA mnemonic?

and have you been introduced to inverse trigonometric functions?

[hazy hollow]

Yes

[charred tundra]

When finding the derivative to this, why should I not use the Quotient rule and instead only take the derivative of them separetly?

Like this

[summer ruin]

this is not a derivative

this is calculating the limit of f(x) as x->1

here they used l'hopital's rule and l'hopital theorem has very specific formulation

[half delta]

yeah when you say "quotient rule" do you mean the quotient rule for derivatives or the property of quotients of limits? there seems to be some info missing that makes your question highly confusing

if you mean you want to find the limit and why not use the limit of quotient property, it's because it gives you an indeterminate form 0/0 so you are stuck, l'hospital's rule (see above) allows you to get out of this and involves taking the derivative of both numerator and denominator, but has preconditions and can't be applied blindly (in this case it is validly applied)

[charred tundra]

thank you so much guys, I misunderstood l'hospitals rule, I thought you took derivative but I see that is not how the rule works

[frank vine]

I did the calculations in my head after finding a few of the cos nx formuas and the step where we find the RE([e^inx), i did some of the work on different n's and then found the pattern

[cedar pawn]

simplification

[old isle]

use arclength formula

arclength=rtheta

[willow bear]

there isn't one

simplification means different things in different contexts

[signal grail]

differentiate h(t)
for rate of change in height

[edgy heron]

what is pre calculus

[willow bear]

a name given in america to various things like trig, exponential functions, and sometimes combinatorics, all packaged into one class to be rushed in a year or so

[signal grail]

i thought calculus was just differentiation and integration 😅

[willow bear]

yes... and?

that doesn't contradict what i said

i described the typical contents of a precalculus class.

[signal grail]

where do we use calculus in combinatorics

[hushed sphinx]

It's the other way around -- "precalculus" is a collection of topics that will later be used for calculus, not something that uses caclculus.

[signal grail]

oh

[crisp bane]

Is series hard?

Im only in precalc

[summer ruin]

yes

[viscid thistle]

depends

hehe

[tardy thicket]

Did i do this correct?

[raw hill]

You confused $-f(x)$ with $f(-x)$ \ \ $-f(x)$ means you multiply $f(x)$ by $-1$, it should be nothing more than distributive property to do this.

[obsidian monolith]

Civil Service Pigeon

[tardy thicket]

Why do you have to multiply it by -1

I got -3

This time

Is this correct?

@raw hill

[raw hill]

$-f(x)=-\boxed{1}f(x)$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

You found $f(-1)$, your answer shouldn't be a constant.

[obsidian monolith]

Civil Service Pigeon

[viscid thistle]

arre yar, civil service exam me calculus hai? arre bhai, ye kiya hogya?

[fossil mango]

hello! i'm reviewing some calculus, and i'd like to clarify the chain rule

i'm insecure in how do i recognize the various functions. each function would be an "operation"?

the power is considered a function?

x^2 the square is the function?

any operation is considered a function until i get the pure x by itself basically?

[summer ruin]

yes

x is the identity

[fossil mango]

which means nothing to me

what's that 😄

[summer ruin]

for any input x the function f(x)=x does nothing and returns the same input

[fossil mango]

oh ok ok

but why 2x is not a function then?

[summer ruin]

it is

[fossil mango]

but i dont use the chain rule there

or do i?

[summer ruin]

you can

[fossil mango]

let me try

[summer ruin]

all these "rules" are true in trivial cases as well as in more complicated ones

because they're proved in general form for any functions

well, differentiable obviously

[fossil mango]

if i use the chain rule with 2x i get.... 2x*1

what im doing wrong?

[summer ruin]

idk, I need to look into your work

[fossil mango]

i was trying to apply the chain rule to 2x

[summer ruin]

let $f(t) = t, g(x) = 2x, h(x) = f(g(x))$, then $h'(x) = f'(g(x)) \cdot g'(x)$, but since $f'(t) = 1$ for any input $t$ you get $f'(g(x)) = 1$ and since $g'(x) = 2 \to h'(x) = 1 \cdot 2 = 2 = g'(x)$

[obsidian monolith]

Transparent_Elemental

[fossil mango]

would'nt it be the same as f(x) = 2g(x) where g(x)=x ??

[summer ruin]

yes

[fossil mango]

ok this makes sense

cool

thank you i think i've got it

so "function" is just any operation on the variable

[summer ruin]

no operation is still an operation

formally a function is something that takes an input and produces some output with the constraint that no input has multiple outputs

other details are irrelevant on how the transformation of the input to output happens

[fossil mango]

thank you

[viscid thistle]

Yes

[lucid trench]

precalc

[boreal cave]

I've just finished vector calculus, moving onto undergrad linear algebra, and we've never used these identities lmao

[lucid trench]

it probably depends on the common cores taught

[violet kelp]

when is cos(x) 0?

[boreal cave]

Honestly tho memorising random obscure identities is a really inefficient way of learning maths and doesn't improve your actual mathematical ability

I honestly think "precalculus" is a scam lol, each subject/area of maths should be learnt properly and not solely for the purpose of calculus

[vapid plaza]

Sum-to-product isn’t “obscure” tho!?

[pine panther]

https://cdn.discordapp.com/attachments/363224154469826562/1060437921351610400/ADE07410-D144-492A-AFA7-14194E63C15B.jpg

How do I solve for these

[willow bear]

@pine panther this image is not loading fsr

can you reupload?

[west cipher]

is there any good way to learn relation and functions, i mean for indian guys from yt?

[primal quiver]

what do you mean exactly

[fossil mango]

hey hello!
I have dy/dx = 1/cos(y) and i know sin(y) = x

i need to get back the x on the right side

my tought was sin^2(y) + cos^2(y) = 1

[willow bear]

are you taking the derivative of arcsin(x)?

[fossil mango]

yes

inverse sine yes

[willow bear]

then you know y ∈ [-π/2, +π/2] and therefore you can say unambiguously that cos(y) = +sqrt(1-sin^2(y))

[fossil mango]

yes, my resoning was: oh it's equal to 1, so i can substitute it on top of 1/cos(y)

sin^2(y) + cos^2(y)/cos(y)

and simplifying i would get only sin^2(y)

[willow bear]

congratulations, you've made your own life more complicated.

no you wouldn't

$\frac{\sin^2(y)+\cos^2(y)}{\cos(y)} \neq \sin^2(y)$

[fossil mango]

aoh yea

[obsidian monolith]

Ann

[fossil mango]

yes yes ok found the mistake lol

i was simplifying the cos as if it were a multiplication XD

ok

thank you 🙂

[lucid trench]

cry about it

[lucid trench]

cry about it

i really don't care what you say so just stop wasting your breath

LOL

I can't yet

But I wanna learn about vectors and matrices and polar equations and mathematical induction

[willow bear]

you could have made your point without the use of "gay" as an insult.

please don't call me bro.

[lucid trench]

I think he's just mad that he never took precalc

[willow bear]

literally have a she/her role
still get "bro"d on a daily fucking basis

[lucid trench]

ok so what

precalculus is my all time favorite math subject

[willow bear]

if you want to yap about the american education system being bad then go to #discussion or better yet #chill

[lucid trench]

and

..You're the only one who has said that

you're kind of a loser ngl

harassing people over what math they're taking

get a life bozo

Im wasting my time with you

[willow bear]

so are the two of you done arguing

[lucid trench]

mhm

[willow bear]

someone pinged me but then deleted their message.

[lucid trench]

reported that idiot

[viscid thistle]

you are an mod/admin, why not check the change-logs

you can see their deleted comment

[willow bear]

i am in fact not a mod nor an admin.

[chilly hazel]

could this code be rewritten in sigma notation

as i increases by 1, the swing distance decreases by 20%, and I am finding what the total swing distance amounts to as i approaches infinity (it is approaching 25)

[summer ruin]

it's just a geometric series

might as well optimize the code by doing math instead of doing for loops

[chilly hazel]

I don't want to code at all, trying to get a solution with pure maths

How would it be written in geometric series

oh that's sigma notation

i haven't taken a calculus class so I am still learning stuff

[summer ruin]

geometric series should be part of the high school program

because it's so simple to prove and use

[chilly hazel]

my school never went past geometry and trig

geometric series was taught in algebra, but not summation notation

[summer ruin]

whatever, summation notation is nothing more than a notation

the results are independent of notation

[chilly hazel]

i have the solution, just need to use summation notation

[chilly hazel]

ah ok

[neon tartan]

What are these symbols?

[summer ruin]

subset and belongs to

[viscid thistle]

Proper subset to be exact

[neon tartan]

I dont know the meaning of it can yall explain plz

[willow bear]

have you done any set theory before?

[neon tartan]

Nope

[willow bear]

set theory deals with sets, which is what mathematicians call collections of objects. a set is defined entirely by what objects belong (or don't belong) to it.
the symbol ∈ denotes this "belonging to" relationship: namely, when we write something like "x ∈ A", we say that the object x (whatever it may be) belongs to the set A.

the concept of "subset" is a bit trickier to explain, because it requires understanding what a set is. but it is a relation between sets, rather than between objects and sets as ∈ is.

we say that A is a subset of B (and write A ⊂ B) if everything that belongs to A also belongs to B.

you might want to pick up a discrete math textbook (or similar) to read more about set theory -- the one you are reading right now probably assumes the reader is familiar with these basic set-theoretic notions, so you'll struggle a lot without that.

[neon tartan]

In the book it stated "c ∈ [0,2]" so that mean c is between interval 0 and 2.

discrete math? I never learn that in school

Thanks for your response.

[slim steppe]

Epsilon

and I forgot what the U is

The epsilon means: belongs with

[hushed sphinx]

Even though the $\in$ symbol is historically derived from the Greek letter epsilon ($\epsilon$ or $\varepsilon$), in contemporary notation (at least since the mid-20th century) they are considered different symbols and it is wrong to write $\epsilon$ when you mean $\in$ or vice versa.

[obsidian monolith]

Troposphere

[willow bear]

the same people who call \in "epsilon" would probably also call \emptyset "phi" and not think it ridiculous

[zinc fulcrum]

lmaooo

[edgy heron]

hello

[viscid thistle]

hello

[edgy heron]

are you good at calculus?

[snow shadow]

Quick question

How do you calculate the tangent of a line

[hushed sphinx]

A line is its own tangent.

[fallen marsh]

for the tangent of a curve though, the derivative

to calculate the derivative you can refer to the limit definition

[viscid thistle]

There is no such term tangent to line, tangent itself is a line, we always say tangent to curve or surface

[surreal berry]

empty set isn't phi? my life has been a lie

[willow bear]

yes it has

[viscid thistle]

No, I am in 10th grade.

[hazy hollow]

whats the answer to the blank

[stone fog]

need help

[sick quartz]

$sec(\theta) = \frac{1}{cos(\theta)}$

[obsidian monolith]

toto but mumble rap

[sick quartz]

look for $cos(\theta) = 0$

[obsidian monolith]

toto but mumble rap

[sick quartz]

because the vertical asymptotes occur at 1/0

[sick quartz]

the first step is to raise both sides of the equation by the log's base (2)

[chilly hazel]

I don't really understand the question

$\lim_{6 \to ?} f(6)$

[obsidian monolith]

Price

[willow bear]

no

$\lim_{x \to 6} f(x)$

[obsidian monolith]

Ann

[chilly hazel]

ohh

so the limit at 6 would be 5?

Or would it be undefined

it has a solid point as well as an undefined point

[willow bear]

no

5 is the value of the function at 6.

the limit of the function at 6 is 0, because that's the point you approach when you evaluate f at points that are close but not equal to 6.

[chilly hazel]

then the limit would be 2 at x=4?

[chilly hazel]

though it approaches, without reaching

[tight swan]

does anybody recommend Advanced mathematics? (Textbook by John Saxon, and is pre calc)

[slim steppe]

The amplitude is the height of the wave

[lofty pine]

Hey precalculus people

I'm curious, how challenging is precalculus to you compared to algebra?

Like is this an easier or harder experience for you

[tight swan]

That will also very much depend on what curriculum

[hazy hollow]

so thos one would be 2 right?

[viscid thistle]

2^2 = 6x + 3

do algebra to find x

[lucid trench]

think of precalculus as algebra 2 on steroids

[pale hazel]

is this aloud? Null factor law, except with not a 0?

[smoky bloom]

?

seems normal

[willow bear]

no