precalculus

[woeful star]

what grade or year are you

[jade sand]

I studied math cuz i was forced, you know default school curriculum, then i didnt opt for it cuz school made me hate it, nom im graduation school on 29th march, and i finally realise i actuqlly love maths

So ye, im not really clear with basics, but i want to study math in deep

[woeful star]

o

[jade sand]

I trying to get my basics clear and also get confy with stuff in maths, prob gonna take an year or two

[woeful star]

do you know trig

[jade sand]

Only the basic six functions, sin coz tan cosec sec cot

[woeful star]

ok

inverse?

[jade sand]

What? Inverse? Idk about that, and i know thats also part of the basics, currently im focusing on algebra stuff, next ill do geometry and trig, but rn im onto algebra

Well, ill study it too. Eventually, until then. Thanks for the help tho

[jade sand]

How to solve this? As in how do i approach this?

[willow skiff]

oh, so like if you try to solve for y in each of these equations

do you get one function, or do you get more than one function (say, square rooting both sides gives you plusminus, so that'd be two functions)

[jade sand]

For eg in first, y=(3x-7)/5. Then y is a function kf x in this case right?

[willow skiff]

by the vertical line test, if one x value gives more than one y, then it's not a function

[willow skiff]

yep!

[jade sand]

Yes, i know, algebraically.

[jade sand]

Wait uh, why do would it get that? Like why would it get a plusminus there?

[willow skiff]

x^2 = 4 gives x = -2, 2 for example

[jade sand]

Oh, rightt, okok, got it 👍. But is there any other way that it might be not a function? Also tysm

[willow skiff]

yeah, so this is the other part

you can deduce that 13 isn't a function but that 14 is

[jade sand]

Yes cuz 150 has two corresponding y values

[willow skiff]

also there's an especially clever way to do q10 which is to just sub x = 0

you get 5y^2 = 4, so by the vertical line test, that's also not a function

[jade sand]

Rightt, okay, i see, intuition is also at play, well anyways, i understood the approach, thanks!

[willow skiff]

yeah so the key is the concept of a 1-to-1 function

x^2, x^4, x^6.... are not 1-to-1

but x^1, x^3, x^5.... are 1-to-1

[willow skiff]

no worries!

[jade sand]

Yeahh, okay.. Ok.., but wait, odd powers still have 1to1 cuz you cant obatin a plusminus situation from them, right?

[willow skiff]

that's what I'm saying, yep

x^5 = k only has one solution, x = k^(1/5)

[jade sand]

Okay 👌

Thanks again, preety much to this entire server, such a big big help in maths to me, a heartfelt thanks indeed

[willow skiff]

no problemo!!

[jade sand]

(:

Alr, so in q8 too, y is not a function right? Cuz x can have both 2,-2

[willow skiff]

no, like if you let x be some number

then 3x^2 is a constant, and let's say that constant is k

so k - 2y = 5 and you only get one value of y for each k

well you could have rearranged q8 to find y, and gotten the same conclusion

[jade sand]

Ohh, right 🤦‍♂️

But, 3x^2 will be 12 both in the case of -2 and 2

[jade sand]

I did, though. Its (3x^2-5)/-2

[willow skiff]

exactly so it's a function

it's just not a 1-to-1 function

also it's y = (3x^2 - 5)/2 but anyways

[willow skiff]

no, to use the vertical line test, you only choose one value of x at a time

you're confusing it with the horizontal line test for 1-to-1 functions

[jade sand]

Oh man, im confused.

Hang on, uh.. So this is not one that has a 1to1 but nonetheless it still is a function

[jade sand]

Right? I felt like that only, i double-checked it into the wrong answer..

[willow skiff]

yep

[jade sand]

Man, ill have to do a lot of work i guess, well its fine i guess

[jade sand]

Oh right, cuz even tho two x values give the same y, no two y values give the same x, right?

[willow skiff]

almost

wait let me read

[willow skiff]

yes that's correct

[jade sand]

Ya know, when confusion gets cleared, it feels like "wow, im so utterly stupid i couldnt understand that much? Yikes"

Lol, anyways, thanks again

[fathom sphinx]

Hola people need help with question 6 🥺. The Inductive step ( ignore question 5 on the whiteboard)

[willow skiff]

your base case is $n = 1$ and thus you want to verify $u_3 = 6u_2 - 9u_1$

[obsidian monolith]

south

[willow skiff]

you need to calculate u3 to verify the base case

[willow skiff]

the inductive step is just showing that:

$$6(n - 1) \cdot 3^n - 9(n - 2) \cdot 3^{n - 1} = n \cdot 3^{n + 1}$$

[obsidian monolith]

south

[willow skiff]

oh well use a different variable k to show this

where k is an integer such that k > 1

[fathom sphinx]

I wish that south was my math teacher 😔

[willow skiff]

wait no your base case is correct

yeah I had something else in mind; you want to prove that the formula works after all for n = 1, 2

https://www.youtube.com/watch?v=yBbKFSLHlFw

there's another example here

and the video explains why you can just sub the formula in

there's two assumptions

[fathom sphinx]

I actualy watched that video 💀

doing a lvl fp1

[willow skiff]

yeah I just found a video that explains better than I can

[fathom sphinx]

ah i see

thx south!!!

[willow skiff]

the assume true for n = k and n = k + 1 bit is important, then you can just draw arrows to where you have used both IHs in the exam

instead of having to write them out in full, as the video has done

[willow skiff]

no worries!

[fallen moth]

hello, I need help with this

it's asking for cos x

I don't know how sin x = -1/2 is sin (-30)

[willow skiff]

mmm do you know the unit circle definition of trig?

that sin theta is the y-coordinate

[fallen moth]

prob not

ohhh sin -30 is sin (360-30)?

[willow skiff]

yep!

follows by periodicity of sin = 360 deg

[fathom sphinx]

south i wanted to ask is it weird how i self study a level math but have only done book questions and not a single past paper (topicals included) i want to start doing topicals and past papers after i finish studying a level math as a whole 😭

[willow skiff]

then you can use ASTC or whatever method you have learnt already

[willow skiff]

that's not weird at all

[fallen moth]

i dont get how it was sin -30 and it suddenly converts to cos at the same value (cos -30)

or is that just how it is?

[fathom sphinx]

oh ayy thx!

[willow skiff]

the proper reasoning is given by the unit circle, and it's a shame you don't learn it in your curriculum

or you could use the graph of cos x and you know it's symmetric across x = 0

[fallen moth]

i probably learnt it but i forgot

it was something like quadrant 1, 2, 3, 4

[willow skiff]

yeah that's ASTC

which I personally don't like

but -30 is the same as 330 (deg), so the 4th quadrant

in the 4th quadrant, only cos is positive

the rest are negative

[fallen moth]

ohh ok

[willow skiff]

so sin(-30) is negative and tan(-30) is also negative

[fallen moth]

yeah it was something like quad 2 tan is neg, quad 3 sin is neg

[willow skiff]

cos(-30) is positive

[willow skiff]

that's the acronym

then quad 1 is everything, or all

[fallen moth]

yeah

ohhh ok i get it now

[willow skiff]

cool

[fallen moth]

hopefully i remember this for my exam tmrw

thanks for your help

[willow skiff]

so it's ASTC actually

[fallen moth]

alright

[willow skiff]

yeah only sin is positive in quad 2
only tan is positive in quad 3

so it's like a huge logic puzzle to figure out which are negative

[fallen moth]

i wouldn't want to know

[willow skiff]

which is why I hate this method and wished that everyone learns the unit circle way

anyways

[fallen moth]

too late to change that now

[rain flower]

hey guys how i solve this question about complex numbers?

[willow bear]

de moivre's thm and/or polar form

[fading monolith]

Multiply top and bottom by its conjugate

[winter comet]

its to the 6th power tho

[fading monolith]

Thought it was a 6 multiplying

Mb

[rain flower]

wait. the 6 is not multiplying?

[winter comet]

yea i wasn't sure what i was looking at at first either 💀

[winter comet]

its raised above the other numbers and it comes after so i think its safe to assume yeah

that's why you'd use de moivres theorem rather than just directly usin the conjugate

[rain flower]

i made this solution. sorry my handwriting is very bad lol

but i think is wrong lol

[winter comet]

<@&268886789983436800>

[winter comet]

that would be more like if it was multiplying by 6 yea

[rain flower]

yeah u right

[rain flower]

could u show me how to solve?

i'm dumb lol

[rain flower]

why u called mod? '-' i did something wrong?

[echo sinew]

I believe he was referring to a spammer, whose messages have then been deleted

[granite ibex]

https://i.imgur.com/Fx7ZrRP.png

cengage making lots of mistakes

2 incorrect problems on my homework now this

xd

[hot crane]

someone help

the derivative rules are too wacky

[willow skiff]

!help

[tender quest]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[willow skiff]

also this is the wrong channel for calculus

[hot crane]

https://media.discordapp.net/attachments/942468162560094228/1068971548440019004/bones.gif

[solar olive]

$-\frac{1}{2} - i \frac{\sqrt{3}}{2} = -e^{i \frac{\pi}{3}}$

[obsidian monolith]

impract1cal

[solar olive]

$\frac{i}{\left(-e^{i \frac{\pi}{3}}\right)^6} = \frac{i}{e^{i \frac{\pi}{2}}}$

[obsidian monolith]

impract1cal

[solar olive]

$= \frac{i}{i} = 1$

[obsidian monolith]

impract1cal

[solar olive]

wait... did i mess up

[elder scaffold]

Guys I’m struggling with function analysis any tips on how I get this stuff down?

[tawdry pilot]

typically this is not a good way to get help. a better way would be to provide a specific example or a more specific aspect of function analysis that you're struggling with. tell us what you understand, what you're good at, and what specifically is tripping you up

TLDR: be more specific

[solar olive]

oh nvm it whould be e^(i pi 2)

which means its i/(-1)

which is -i

woops!

i

[jade sand]

How to tell if a function has a constant or changing slope, also, do we normally grapg functions with nonconstant slopes or we can put that to the computer

Oh and come to think of it, what is it in a relation that it is not used in calc but only a function is

[jade sand]

Also, how do i write this grqph's range. Its domain is [-3,2] but range? Should i write it as [-3,-2],[-1,3]?

[willow bear]

$[-3, 2) \cup [-1, 3]$. it's a union of two intervals -- and mind the upper endpoint of the first one as it's excluded

[obsidian monolith]

Ann

[jade sand]

Oh, right, its a hollow circle, thanks!

[dusk fiber]

Have you studied differentiation yet?

Basically, if the variable has the power of 1 then has a constant slop

[jade sand]

Ohh, ok, that makes sense

[dusk fiber]

Constant slope means a straight line

[jade sand]

Yes, i know

So, say we have something like x^(2)+x?

Would that mean it has a nonconstant slope

[dusk fiber]

Yes

[jade sand]

Alr

[opal sparrow]

is this alright?

[lapis sparrow]

It would be alright if you took the integral of x from sin to cos, then converted the I into the u from x^2. Make sense?

[fathom sphinx]

Hi for question 8 is my working for on the Inductive step correct? (My book doesn't have a markscheme : ( )

[rocky wind]

these aren't real induction question
cuz induction isn't necessarily needed
there's certainly an alternative way to find the sum (without knowing it in advance)

[inner topaz]

i mean any question isnt a real induction question based on your logic

[brazen scaffold]

ignore the integral sign bit

which partial fraction form can this be rewritten in

[echo sinew]

$$\frac{A}{x + 1} + \frac{B}{2x - 3}$$

[obsidian monolith]

Alberto Z.

[echo sinew]

But first you need to perform polynomial division

Because you can do partial fractions only when

deg(numer.) < deg(denom.)

[stark ether]

ugh can someone pls help

this is bothering me sm

tangent graphs

[willow skiff]

what happens if you sub in x = 0 into all 4 equations?

[wanton isle]

You just want the answer or an explanation

Cuz i kinda suck at explaining

[inner topaz]

well if you want an actual understanding of what is going on ignoring the +140 note that the period of tanx is $\pi$, which means the graph normally repeats itself after pi times, but instead we have $\frac{\pi}{6} x$, we let that = $\pi$ to find the period

then the multiplication by 140 outside simply stretches the whole thing by 140 vertically (ig u can imagine a long tall but thin rectangle), note that if it was negative it would also flip the graph of tan

then at the end you move the whole y value up by +140

[obsidian monolith]

Ryse

[lament glacier]

what the freak

[warped shuttle]

how to solve this limit ? i got a 0/0 even after L'Hôpital's rule

[lean cove]

Make sure you get an intederiminate form then repeatedly apply L Hopitals rule until it works or you do not have an intederminate form

[uncut mulch]

difference of two squares / conjugates
similar idea with difference of two cubes

[chrome inlet]

Answer is 1 not zero

my bad

I forgot math

[uncut mulch]

why did the limit change from 1 to 0, also don't just give away fully worked solutions and/or answers like that

[chrome inlet]

Ok

Oh ya

Silly mistake

[chrome inlet]

Should I delete it?

[uncut mulch]

yes

[warped shuttle]

how would this apply to the question ?

[fading monolith]

A hint to solve the limit(?

[warped shuttle]

well i know but can't figure where to use difference of two squares rn

[fading monolith]

a^2-b^2=(a-b)(a+b) and you have there a-b form so

[dusk fiber]

Use it again

[sturdy hound]

can someone check if i got the right answers for this problem:
T_B_ = 2169.5157 lbs
T_A_ = 3611.1112 lbs

[fallen moth]

I need help with this please

[south hemlock]

a common Trick with square root limits is to multiply by the conjugate

[fallen moth]

what's a conjugate

x+6?

[south hemlock]

the conjugate of a+sqrtb is a-sqrtb

[fallen moth]

hwo would that look like?

[south hemlock]

Try to bring it into the form above

[fallen moth]

a=1 and b=-10?

[south hemlock]

umm

Not quite

[fallen moth]

hmm

[fallen moth]

ohhh

I remember the formula is something like

b-q/2 sqrt a

[south hemlock]

umm

I don’t quite get where you’re trying to go

[fallen moth]

oh that's what my friend told me

[south hemlock]

However i believe this trick in this case doesn’t help that much

[south hemlock]

I would suggest you take out an x2 of the inner expression in the root

[fallen moth]

alright

[south hemlock]

Can you post your work after you’re done

[fallen moth]

yeah I posted it on a help channel

my friend helped me through messages

I still don't understand much though

[wheat oar]

Will there ever be a case when A¹A = I but AA¹ ≠ I? I'm trying to figure out if I need to perform the verification twice for each of these expressions...

[winter comet]

they are both true simultaneously

you would only need to verify one and that would mean the other is true as well

if A^(-1)A = I, then A(A^(-1)A) = A ->(A A^(-1))A = A, and you know IA = A, so A A^(-1) = I

assuming associativity of matrix multiplication and just the uniqueness of matrices lol

[inner topaz]

think this would go in group theory but yes it will always be true

[winter comet]

why group theory?

[inner topaz]

in every group a * a^{-1} = a^{-1} * a = e
a is any element belonging to a group
e is the identity element

ig this doesnt apply if the det is 0

but ignoring non singular matrices matrix multiplication forms a group under multiplication i believe

[wheat oar]

This simplifies to AI = A and IA = A but matrix multiplication is not commutative so how does this prove that the order doesn't matter?

[wheat oar]

This problem is from a pre calc textbook

[winter comet]

matrix multiplication is associative, so A (A^(-1) A) = (A A^(-1)) A
you can simplify this to AI = IA, but this assumes that A^(-1)A = I and that A A^(-1) = I

but if we just assume AI = IA = A is true, then it implies that A^(-1)A = I and AA^(-1) = I

I don't see why group theory is needed unless I'm assuming things from group theory, I wouldn't know if I was :l

[inner topaz]

i mean group theory is only needed here for associativity and inverse but yeah not rly needed

[winter comet]

can't you just prove associativity element-wise lol

[wheat oar]

Oh okay this makes sense when you set them equal to each other! Thank you!

[sturdy hound]

i need help with this problem:
also ignore my writing on the picture but this is my work and i just wanna confirm if i am right
240cos(30 degrees) + 110cos(-25 degrees) + xcos(0 degrees) = 500
x = 192.4600, so bill neds to pull 192.4600 pounds in order to move the boulder
is the method i used correct?

[raven laurel]

i had that exact fucking problem in my textbook like 3 months ago

Can anyone here explain mathamatical induction?

[sturdy hound]

i can, but i can probably explain it better if u have a specific problem u need help with

[late silo]

What's weird is I never learned matrices in pre-calc. I have no idea how to find inverse or even what that means. I don't even know the point in a matrix other than for solving systems of equations, which is more for algebra than calc.

[winter comet]

you don't need to, you learn it all in linear algebra anyway lol

[late silo]

Oh yeah? Ok then I feel happy again lol

[winter comet]

XD

[cursive glen]

Anybody here?

[celest rock]

?

[cursive glen]

I got a question I need help on

Would it be simplified to -15?

[celest rock]

Squaring never results in a negative number, it's 15

So it's 15+49=64

[hybrid plinth]

do you learn matrices in algebra 2 or precalc?

[willow bear]

definitely precalc if at all tbh

[fleet ridge]

unsure if this is algebra or precal but what on earth are multiplicities

like i get it but i dont

im using it for zeroes for polynomials but ig the questions are worded pretty oddly

from what i gathered it's the exponent of the factors once completely factored out?

[astral apex]

pretty much

like the multiplicity of the root x = 3 of f(x) = x(x - 3)^4 (x - 5)^2 is 4

and the multiplicity of x=0 is 1

and of x=5 is 2

[lean imp]

i need some help for my pre calc test 😭 if anyone can help me in #help-22 i would appreciate it

[astral apex]

and for roots with odd multiplicity, the polynomial's graph "passes through" the x axis at those

for even multiplicity, the graph "bounces off" them

[storm lodge]

yo

i can

[formal wren]

Help

[willow skiff]

I see you've written some work out

what do you get if you let f(x) = g(x) then simplify

[formal wren]

Lemme see one sec

[formal wren]

You get sin^2 x= cos^2 x +1

[willow skiff]

yeah, and is that an identity or not

[formal wren]

I mean yeh Pythagorean but they won’t equal the same thing

It will be - and positive

[willow skiff]

it's not the Pythagorean identity

yep cause of what you said

sin^2 x - cos^2 x = 1 is not sin^2 + cos^2 x = 1

[formal wren]

Wdym?

Ohh yes

[formal wren]

So it’s not identity?

[willow skiff]

yeah, no identity is the answer

[formal wren]

Eyyy

[formal wren]

Thank you

[formal wren]

@willow skiff I have a question for this function, why is there a phase shift im so confused

[normal gale]

If w = cos (theta) + i sin (theta), show that (w-1)/(w+1) = i tan (theta/2)

[willow skiff]

Cos has a maximum at t = 0

So the maximum is shifted 3 to the right

[willow skiff]

What did you try?

[normal gale]

nothing yet, my math teacher is gonna check the answers tmr

[sleek jay]

I am a bit late here but in the calulation, the square and square root of 15 cancels out resulting in 15, -7^2 = 49, so the answer is supposed to be the square root of 64 which is 8

[normal gale]

It can be shown that $\int (e^{ix} \cdot e^x) dx = \frac{1}{i+1} e^{(i+1)x}$, find $\int (\cos x \cdot e^x) dx$.

[obsidian monolith]

preciousnectar

[jaunty tendon]

(unit circle) hello, theres a given where sin = 2 sqrt of 3/3 and cos = negative, ive tried tracing sin back to 2/sqrt of 3, but that makes h lower than o, what am I missing?

[hollow pasture]

https://youtu.be/a1GrVJyOTaA

[willow skiff]

yeah there's an error in the question then

[willow skiff]

can you take the real part of 1/(i + 1) e^((i + 1)x)?

[fathom sphinx]

South is it possible to self study discrete math?

[willow skiff]

yes

[fathom sphinx]

Ah alr thx South!

[jaunty tendon]

well that sucks theres 4 more questions exactly like it 😕

[willow skiff]

[jaunty tendon]

how about if cos = sqrt of 7/9 and csc is negative? is it solvable?

[willow bear]

ok real quick.

you should use parentheses, and not the word "of", when writing stuff with roots in plaintext.

[fathom sphinx]

is it possible to self teach undergraduate and postgraduate level math. (With digital textbooks, videos and such.)

?

[willow bear]

we don't know if \verb|sqrt of 7/9| means $\sqrt{\frac{7}{9}}$ or $\frac{\sqrt{7}}{9}$ --- these are more properly rendered in plaintext as \verb|sqrt(7/9)| and \verb|sqrt(7)/9| resp.

[obsidian monolith]

Ann

[willow bear]

postgraduate? highly unlikely.

[fathom sphinx]

Oh I see thx Ann!

Wth is the difference 😭

I legit don't knowwww

Oh nvm postgraduate is after a degree or smth

[willow bear]

undergrad is when you're working towards a bachelor's

postgrad is anything that comes after

[jaunty tendon]

oh sorry, that is how we write it in online exams and thats how we were taught for 6 years, its cos = sqrt(7)/9

[fathom sphinx]

Oh I see thanks for the explanation.

[willow bear]

cos(theta) = sqrt(7)/9

[fathom sphinx]

Ann are you post grad and if so are you aiming for a PhD!!

[willow bear]

you could have just @'d me instead of replying to a completely irrelevant message

and also, frankly, that's none of your business whether or not i'm going for a phd.

[fathom sphinx]

Whatever

[late nimbus]

i wanna start teaching myself precalc. how and where should i start

[plain marten]

trignometry

teach your self a lot of trig

[soft flare]

As the guy before me said u need trig but also algebra if u want i can send you some of the stuff i used to teach myself the basics of pre calc

[late nimbus]

sure pls do

[soft flare]

This is the one I used

wait it might be too big

[soft flare]

nvm

also go on this website called desmos

its probably one of the best tools for learning alot of preclac

[raven laurel]

its not a specific problem i just dont understand it at all

[sturdy hound]

basically for me i have to do proofs proving that both sides are equivalent or that the equation is divisible by a number or a multiple of a number

u start out with the normal equation p(n)
then u do p(#) to prove that when u plug in a number it is right
then you change the variable n to k and write out p(k) and assume it is true
then you change the variable from k to (k+1) and write out p(k+1), and you have to make p(k) appear within that equation so you can plug it in and then prove it

its easier if i have an example to show u

[wheat oar]

A Pre Calc textbook is a good option. The big pre calc textbooks are used to teach classes in both pre calc and trig

[celest nacelle]

Same 💀

There is also a pre calculus chorus on YouTube if your interested I will link it down below 😄

[brazen scaffold]

in the uk?

yep

[soft flare]

yes

[silver mist]

How would you find the inverse of this equation?

I got (log_2(x+5/4))/3 = y

[summer ruin]

this is correct

[muted hinge]

Is greater than / less than defined for complex numbers

[river drift]

there are ways to define an order but none of them behave nicely with arithmetic the way that the ordering of the real numbers does

[willow bear]

no

it is in fact impossible to define such a notion on C and have it play nicely with complex number arithmetic

[neon steppe]

720 seems reasonable in the sense that you can arrange in 5! ways and then partition them into two 🤔 Though having asked chatgpt and alike it consistently seemed to bring up 3840 as the answer, in which it takes the total distributions 32 and multiplies it by total arrangements 🤔

but like 120 x 6 already accounts for every possible arrangement right?

[wanton isle]

Guys how do i solve this: Use De Moivre's Theorem to find (1 + ∛i)6

Its the sixth power btw

[willow skiff]

which cube root of i? the principal cube root?

[wanton isle]

If i understand principal cube root correctly then yes

[willow skiff]

great, so write i^(1/3) in Cartesian form

then add 1 and convert back to polar form

[wanton isle]

Hold up how do i change it to polar form when the i is cube rooted

[willow skiff]

you should get i^(1/3) = (cos pi/2 + i sin pi/2)^(1/3) = cos pi/6 + i sin pi/6 first

[wanton isle]

Oooooooooooooh

Yeah that makes sense now

And how do i add the 1?

Hold up i think ik how to

[tired garden]

what even is the question?

[wintry rover]

<@&268886789983436800>

[viscid thistle]

What was there

Seen a lot of those

Their account got hacked

[deep crystal]

somewhat important

[wheat oar]

Being able to picture the graphs of the six trig functions helped me a lot. I remember spending a day or two playing around with transformations questioning if I was wasting my time but it turned out to help give a lot of natural intuition when solving trig identities. I haven't started calc yet so I can't speak to how much it helps in that department.

[warped shuttle]

how to evaluate this limit ?

[remote cove]

Hello guys

[willow bear]

$\lim_{x \to 0} \frac{x \floor{2/x} - x - 2}{x}$ this?

[obsidian monolith]

Ann

[remote cove]

I have bunch of doubts from this video could anyone help to resolve my doubts

https://youtu.be/S0_qX4VJhMQ?si=QjN98dRKz6t6myxt

[willow bear]

you're probably best off posting your doubts (along with the video) in a help channel.

[remote cove]

Send that channel

[willow bear]

read #❓how-to-get-help for instructions.

you should take any chanel with a name like #help-[NUMBER] which doesnt have anybody else's username on it

[warped shuttle]

yep

[willow bear]

well the $-x$ can be pulled out and so the function will turn into $$\frac{x \floor{2/x} - 2}{x} - 1$$

what have you done so far for it tho

[obsidian monolith]

Ann

[warped shuttle]

at first i wanted to try the l hopital rule but the floor function is in the way so i'm kinda stuck

no progress per say

[willow bear]

l'hop is inapplicable because floor(2/x) is discontinuous in too many places

[warped shuttle]

yea ik that's why idk what to do

[willow bear]

the fraction can be simplified as floor(2/x) - 2/x

which is -frac(2/x)

[warped shuttle]

where did the -1 go?

[willow bear]

it didnt go anywhere i just didnt mention it

i said "the fraction" meaning (x floor(2/x) - 2)/x

the -1 stays as is and doesnt rly spoil anything for us that much

[warped shuttle]

the range of floor(2/x) - 2/x would be 0 to -1 right ?

[oblique raptor]

[2/x] can be written as 2/x , so the form is 0/0

U can use L hospital rule

Is the ans -1?

[warped shuttle]

why ?

[willow bear]

floor(2/x) is not equal to 2/x...

[remote cove]

@willow bear what does tiny nudges means?

[willow bear]

no, the numerator has too many discontinuities

[willow bear]

i literally do not know how else to explain it. look up "nudge" in the dictionary idk

sorry

[remote cove]

What does nudge mean in google it says a push to someone but whatd that wanna do in derivative

[warped shuttle]

give the full context

[remote cove]

3b1b repeatedly says tiny nudges are the heart of derivatives

In his video

What does nudge means?

[warped shuttle]

tiny parts

[remote cove]

Oh okk

[oblique raptor]

One of my teachers told me that when a gif function is tending to infinity it can be written 2/x

[willow bear]

gif function 💀

[oblique raptor]

We can write [f(x)] = f(x) - {x} and if the limit on [f(x)] tending to infinity, u can ignore the fractional part cuz its range is too small [0,1)

[warped shuttle]

but the answer isn't -1 and it's undefined

[pastel mountain]

hellloo

[mint cedar]

Greetings.

[pastel mountain]

I’ll send the problem

I understand how to get my HA,VA, x int, however i have a difficult time figuring out my y int and hole

I’ve done so many problems and I’ve only been getting my y int and holes incorrectly, so I just want a review of how I can get my y int and holes

[mint cedar]

I don't think there is a y-intercept.

Since the function is undefined when x = 0.

The hole should be at x = 0 too, and you should be able to get the y-coordinate using L'Hôpital's rule.

[pastel mountain]

0 is undefined right?

Or no?

[mint cedar]

When x = 0, the denominator becomes 0, and you cannot divide by 0.

$f(0) = \frac{0}{0}$

[obsidian monolith]

arvin

[mint cedar]

So yes, undefined.

[pastel mountain]

Okay thank you

[blazing canopy]

Nice hole

[bleak forge]

how do you do the derivative of sqrt(e^x-1)

[gaunt pumice]

chain rule

[willow bear]

⛓️ 📐

[bleak forge]

i dont understand how please explain

also explain how you came to that conclusion, that you had to used the chain rule

[winter comet]

composite function

[willow bear]

ok first off: is it $\sqrt{e^{x-1}}$ or $\sqrt{e^x - 1}$

[obsidian monolith]

Ann

[bleak forge]

Second

[oblique raptor]

Its a composite function so chain rule

[remote cove]

Where can i ask my calculus doubts?

[river drift]

#calculus ?

[uncut mantle]

Is this Newton

[willow bear]

offtopic posts go in #chill

[rancid bluff]

This is not a homework assignment just trying to see if I understood the material correctly. Hope I'm posting in the right channel.

So for the mean rate of change, it measures how much a function changed in a specific interval, right?

So for example if I were to say that in 40 minutes I drove 40 kms. And I need to figure out the how much the graph changed I do it like this? Stupid question, but how do I know what numbers to put into the formula= f(x)=x²+px+q , its the right one, right?

Also how can I read graphs correctly? Where is the turning point etc.?

[queen grail]

e^iπ + φ^2 - φ = 0

[next drift]

how do i do this

[fierce viper]

Is a three days enough to study for my pre cal test on trig functions

[winter comet]

are you actually curious or just looking for some motivation

[fierce viper]

I’m actually curious

Okay how about four days

[winter comet]

then its a very vague question 💀

depends on

1. where you are now
2. what your test will cover
3. how fast you can learn it
   and we know...none of these

XD

[winter comet]

I would say probably...? but I really have no idea 😁

[fierce viper]

Is this easy

Is this a four day thing

No it’s not it looks easy

[winter comet]

it doesn't look bad

[fierce viper]

So it’s a three day

Thing

[viscid thistle]

have you learnt sin= p/h etc for every identity?

[willow bear]

p/h ?

[winter comet]

popposite/hypotenuse

[viscid thistle]

perpendicular /hypotenuse etc

[viscid thistle]

he/she needs to learn those identities for that

[willow bear]

she's got the pronoun role diamond for she/her

but even if m didn't, you should never say he/she like that

singular "they" is a thing

[fierce viper]

Yes I know all of them

[viscid thistle]

I didn't see sorr

[viscid thistle]

cool just practice more you'll ace it

[primal iron]

does anyone have practice questions for year 11 precalculus i have a test tmr and i haven’t studied anything 😭

[willow skiff]

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

https://madasmaths.com/archive_maths_booklets_standard_topics_trigonometry.html
https://madasmaths.com/archive_maths_booklets_standard_topics_various.html

these are more exam-style

KA is more quizzes

[primal iron]

thank youuu (:

[willow skiff]

no worries!

[whole void]

what’s it on

[abstract grail]

What is this math

[brazen scaffold]

your in the uk?

[merry tide]

Pre calculus

[abstract grail]

What is pre calculus

[merry tide]

The math you learn to prepare for calculus

Which are things like algebra, functions, trigonometry

[abstract grail]

oh, can you give me some examples?

[dry lantern]

graphing functions on polar curves

Trig identities, like sin(2x) = 2 sin x cos x

[formal bronze]

Can someone explain to me how the answer is -5?

[willow skiff]

which part are you confused on?

[formal bronze]

The answer (-5), I solved it entirely up to the last step before the answer

[willow skiff]

right, and do you see how -8/12 simplifies to -2/3?

[formal bronze]

Ohh yea

Thank you

[willow skiff]

no worries!

[formal bronze]

So if am correct we simplified eight to -2 then we divided -2 with 10 to get -5, correct?

[willow skiff]

yep, so you would just do $\frac{10/3}{-2/3} \cdot \frac{-3}{-3} = \frac{-10}{2}$ to simplify the fraction

[obsidian monolith]

south

[willow skiff]

the big thing with fractions is you need to multiply/divide the top and the bottom by the same number

then you're guaranteed another equal fraction

well like don't multiply or divide by 0 but everything except that

[formal bronze]

To get a common denominator right?

[willow skiff]

here you already have a common denominator

so you want to get rid of the common denominator so that you simplify it

10/3 and -2/3, common denom is 3

[formal bronze]

Ohh okay

[willow skiff]

well if you don't mind 10/(-2) = -5

then that also works

[formal bronze]

Tysm this really helped me

[willow skiff]

no worries!!

[formal bronze]

🙌

[primal iron]

nooo i’m in aus also sorry for the late reply i just got home

[primal iron]

it was on functions and graphs and symmetry i think but it’s too late now it’s all goods tho i have time for my next test to figure it out lol

[viscid thistle]

i do!

this or evb in this server

i 100% recommend

u use this website

https://www.kutasoftware.com/freeipc.html

gives you worksheets, with answer keys

for ever pre-calc topic

it also even has calc there too

[stone cloud]

For this question, why is the first solution wrong and we have to convert to sin^2x

[old garden]

lim x-> 0 (tanx/x) = 1 .
Here if theta tends to 0, cos^2theta would be 1 and thus it would be tan(pi)/pi

So you can't use it here

[stone cloud]

Ok thanks

[swift creek]

gys i think that's equal to 0?

[crisp fjord]

hello can someone help me with proving derivative of csc(x)

[winter comet]

with other derivative rules or with the limit definition of derivative?

[crisp fjord]

i get to lim h approaches 0 1/sinxcosh+sinhcosx-1/sinx/h and am stuck

[winter comet]

ah

[crisp fjord]

all vids i watch dont make sense

pls dont make fun i am to new to this and am only 12

[hoary iris]

,, \lim_{\alpha \rightarrow 0}{\left(\frac{\sin{\alpha^{n}}}{(\sin{\alpha})^{m}}\right)}

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

I have reduced this to $\lim_{\alpha \rightarrow 0}{\alpha^{n-m}}$

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

My book says 0 if n>m

Infinity if n<m

But 1 if n=m (how?)

[winter comet]

consider lim n-> 0 [n^0]

[hoary iris]

0^0 is indeterminate form, isn't it?

[winter comet]

wrong thing

i meant n^0 lol

[hoary iris]

Yes but

Oh yes i understand

We are approaching not plugging zero

[winter comet]

mhm

[hoary iris]

Ok thank you

[hoary iris]

Why do you need big lego brick?🤣

[winter comet]

well I certainly don't need small one

[hoary iris]

🤣

Are you doing undergraduate math?

[winter comet]

I guess it's considered undergraduate

[hoary iris]

Are you self learning?

[winter comet]

no i'm taking classes

w dual enrollment

well i mean it involves self-learning but i don't think thats what you meant 😂

[hoary iris]

Math with what?

[winter comet]

what?

[hoary iris]

The other course

[winter comet]

the math i'm taking?

[hoary iris]

What does dual enrollment mean?

[winter comet]

ohhh it means I take hs classes and classes at local community college

well i suppose it doesn't have to be community but mine is 💀

[hoary iris]

😁

Have gone through calc 1?

[winter comet]

yeez

[hoary iris]

What are the math courses you're taking?

[winter comet]

just LA this semester

i mean physics too but physics doesn't count as math but it should

[winter comet]

what are u taking?

[hoary iris]

I am a high school student of grade 11(In India though)

[winter comet]

oooh nice

are you going to take the JEE

💀

[hoary iris]

It has basics of calc i suppose

[winter comet]

death 💀

[hoary iris]

I want to enroll in MIT or yale University for math

But my parents want me to write JEE

[hoary iris]

Is it possible?

@winter comet Do you think is it possible?

[winter comet]

what is possible?

to get into those colleges of course its possible

[hoary iris]

To pursue math in mit

Or yale University

[winter comet]

yes its possible, although it requires a lot of work + luck XD

[hoary iris]

Does it really require extra curricular activity?

[winter comet]

I don't know

XD

[hoary iris]

thank you xd

[winter comet]

i'd say the more you do the better off you are probably

I hear people say extra curricular activities are good and then i hear the colleges saying just do what you are passionate about and honestly just do both if you can 😂

[winter comet]

🔥👍 but where the 👍 is a jalapeno

no

some other kind of pepper

[hoary iris]

Yeah I suppose

[arctic dagger]

🌶️

[winter comet]

that

[hoary iris]

Yeah probably

Can we take limits inside log of some function? @winter comet

[winter comet]

you can take limits inside of continuous (composite) functions if the limit exists... otherwise i don't know what you mean

[vast quartz]

I'm not viper, but just go to the college that you realistically think will get you the best mathematics education for you personally.

I'd genuinely prefer a state university over a T20 for numerous reasons, and I've confirmed my enrollment to one, happily.

[winter comet]

only viper can have the ultimate knowledge about this ofc so your opinion doesn't matter

but i agree with you

jkjk

[vast quartz]

The expectation of going to a T20 to be successful in your academic field is just nuts

There are Nobel Prize winners who graduated from state universities 😭😭

[hoary iris]

What are state universities?

[vast quartz]

Sorry, I assumed you were American since you were asking about MIT.

[hoary iris]

No, I am indian.

[winter comet]

<5% of people in the world would be successful in their academic fields if that were the case

[vast quartz]

State universities are universities in the United States that are publicly funded by the state (equivalent to a province, district, prefecture).

[hoary iris]

Is MIT a state university?

[vast quartz]

Not even remotely close

It's a private university, meaning it is not funded by its state

And it's a T20 school (top 20)

[hoary iris]

Yeah I had heard about it.

[hoary iris]

Yes

[vast quartz]

State universities are generally viewed as lesser than private universities because they get less funding, are smaller, less selective, and lesser known

Historically, most people who are famous in their fields went to a T20

Imma quit yapping now

[hoary iris]

A comman man can't?

@vast quartz Eclipse ryu?are you here?

[winter comet]

can't what?

[hoary iris]

Enroll in T20?

[winter comet]

they can

i don't see the logic

[hoary iris]

She says historically most famous ones went to T20

[winter comet]

most

which implies some did not

[hoary iris]

Is community college different from State University?

[winter comet]

yeah community college usually just has the lower division early undergraduate classes (one's you'd take in the first 2 years) and then people can transfer to four year colleges for upper-div

i think thats how it works ish

[hoary iris]

,, \lim_{x \rightarrow \infty}{\log{\left(\frac{x+a}{x}\right)^x}}

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

@winter comet I will make inside as 1 + a/x

Then can I take lim inside log

?

[winter comet]

no

cuz the x is still outside

[hoary iris]

,, log{\lim_{x \rightarrow \infty}{\left(\frac{x+a}{x}\right)^x}}

[obsidian monolith]

Monkey•D•Luffy

[winter comet]

lim x->a f(g(x)) = f(lim x->a g(x)) if lim x->a g(x) = L exists and f is continuous at L

[hoary iris]

Like this

[winter comet]

i take this to mean (log( (x+a)/x ))^x, not log ( ((x+a)/x)^x )

it could theoretically mean either one but typically it means the first one

[hoary iris]

No no second one

[winter comet]

oh it is the second one?

[hoary iris]

Yes

[winter comet]

then yeah you can do this as long as that limit exists

[hoary iris]

Thank you

@vast quartz is Indian University as equal as state universities of america?

[west arch]

yo i need help with a probabilities

exercise

[willow skiff]

equal in what way?

[granite sigil]

I forecasted for precalc can someone tell me what to expect? I want to make sure I’m making the right choice

I enjoy algebra and find it easy once I learn the formulas and techniques

But I literally HATED geometry/trig

Is it similar to algebra?

[willow skiff]

precalc is more algebra and deeper

[granite sigil]

Oh ok!!!

[willow skiff]

well it takes an adjustment period for sure, because the central theme in precalc is functions

you may know functions as graphs and indeed precalc has a million graphs

but the idea of a function is actually more something like this:

it's just a rule that you apply

you put in a number, apply some consistent rule, then get an output number

[granite sigil]

Oooo

That looks fun

I enjoy math I just get frustrated easy

[willow skiff]

also the higher up you go in maths the more you'll be expected to learn the how and why

so not blindly applying formulas

[granite sigil]

Oh cool!

[willow skiff]

practicing loads of different question types to make sure you patch up all the holes in your understanding

[granite sigil]

That’s nice

[willow skiff]

but yeah this is actually general study advice for at least all of STEM

[granite sigil]

So precalc seems like a good fit for me then

[willow skiff]

yep absolutely

[granite sigil]

Why continue to take math classes if you don’t learn new stuff is what I say

That’s why I’m not taking stats

[arctic dagger]

,w riemann sphere

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[arctic dagger]

i think I've seen this in wikipedia

and it like shows how conic sections are just the same

like they're just all ellipse?

parabola: an ellipse with the other focus (?) on infinity

and yea hyperbola is like an ellipse wrapped around the sphere

i didn't try to understand it but that's what i got skimming the page

yea that's really interesting

so it's riemann sphere, i see. i didn't remember it

it really caught my interest

i could use it as a motivation to learn about it

true

[haughty iron]

oh lol fogot to attach question

[arctic dagger]

the decimal form of ⅙ is 0.166666…

[haughty iron]

yeah i realised after posting 😆 thanks man good day!

[knotty goblet]

Hello

Is anyone there

[wild bramble]

yes. no. no longer. bye (why am i even awake at this time br ts pmo

[leaden cave]

Hi there! I just have a really quick question I noticed that in this Calculus course I am taking that there is this formula which is put as delta f/delta x I was wondering if this is the same as delta y/delta x

[arctic dagger]

it is

y=f

y=f(x)

they're just names at the end of the day

you may use different letters

[leaden cave]

Ah okay, thank you very much!

[arctic dagger]

the top one is the dependent variable, and the bottom one is the independent variable

[haughty iron]

why we shift graph right when the graph fxn is y=f(x-c)

same for y=f(x+c) we shift graph toi left

[strong flicker]

try evaluating a few values for f(x) = x^2

and f(x-3)

particularly, f(0) = 0 so the x-intercept is at (0,0)

now,
f(x-3) = (x-3)^2
to get the x intercept, we need (x-3)^2 = 0 which means x = 3
so the intercept was shifted to the right by 3 units

[haughty iron]

okay i did its comes +ve always

[strong flicker]

now this applies to all values for x in domain
so there is a rightward shift

[haughty iron]

ohhh i get it thnx little bit straight line concept huh!!!

thanks so much

[hoary iris]

Equality in their approach in mathematics department

[winter comet]

are indian universities equal to each other?

[vagrant raptor]

I have a couple math professors that have degrees from Indian universities. They usually come to the US to get their doctorate though

as far as I know, if you're asking "does my indian degree have meaning in the US", the answer is that as long as it's a proper university then yes

[celest nacelle]

well said

[vagrant raptor]

It goes for anywhere, really. I would look for people that have graduated from your university and see if they've had success in foreign nations, or even within your own nation

Not sure who asked the original question, but if you're curious I can grab a couple of the universities that my Indian professors went to

[karmic karma]

helps please

[winter comet]

what have u tried

[hoary iris]

No the way of teaching Mathematics is best in which side?

[willow bear]

@karmic karma do you still need help with this

[karmic karma]

no

i dont

thanks!

[willow skiff]

The US

In India a lot of the mathematics courses have been cannibalised by engineering

Consequently there aren't many course options for pure maths in India

But teaching quality between the two countries I believe doesn't substantially differ for the top Indian and US unis

Where it does differ is that smaller US colleges will definitely be stromger

[boreal wharf]

a^-∞ is 0?

[willow bear]

if a>1, sure

though this is a slight abuse of notation

[safe basin]

kinda wild notation

[boreal wharf]

I see

Is
lim b-> ∞ a^b better or is it just the same

[safe basin]

yeah how you should be saying it is like lim_x->infty a^-x = 0

or you could say a^-x -> 0 as x -> infty (less formal but like still understood if you're explaining something)

and specify that a>1 as well

[hoary iris]

Yeah true

[lyric cradle]

Why is the derivative of a function zero at the maxima and minima of a function. Is there a proof I can follow as a calculus freshman

[willow bear]

have you seen the limit definition of the derivative?

you can reason using that and it isn't terribly hard

[lyric cradle]

The first principle?
d/dx = (f(x+h)-f(x))/h
h tending to zero?

[willow bear]

yes, the first-principles thing

ok, so

probably easiest to just take you through the proof right here and now

let $c$ be an extremum point of your function. we assume $f$ is differentiable at $c$ (ie $f'(c)$ exists), and also let's say that $c$ is a local minimum for your function. (the case when it's a local maximum will proceed similarly, just with some signs reversed)

[obsidian monolith]

Ann

[willow bear]

consider the one-sided equivalents of the limit that defines $f'(c)$, namely:

$\lim_{h\to 0^+} \frac{f(c+h)-f(c)}{h}$ and $\lim_{h\to 0^-} \frac{f(c+h)-f(c)}{h}$.

these two are equal of course, but it will help us to reason separately about each one.

[obsidian monolith]

Ann

[willow bear]

@lyric cradle do you follow so far

[lyric cradle]

Yes

[willow bear]

ok right

now for the right-hand limit

the numerator, for h close enough to 0 (and thus c+h close enough to c), will be positive or 0, because f has a local minimum at c and so f(c) <= f(c+h).

the denominator will also be positive because h goes to 0 from above.

thus the fraction as a whole is positive and we get $f'(c)\geq 0$.

[obsidian monolith]

Ann

[willow bear]

does that make sense to you?

[lyric cradle]

Yes

[willow bear]

for the left hand limit the logic is almost the same: the numerator is positive and the denominator is negative

so the whole thing is negative and so $f'(c)\leq 0$

[obsidian monolith]

Ann

[willow bear]

so f'(c) has to be <=0 and >=0 at the same time

it has no option but to be 0

[lyric cradle]

Thank u.

[willow bear]

for a maximum, the logic will be the same only the inequalities will be the other way around

[hoary iris]

Can I prove the limit $\lim_{x \rightarrow 0}{\frac{\log{(1+x)}}{x}}=1$ using the binomial expansion of log(1+x) as well as using the result $\lim_{x \rightarrow 0}{\frac{e^{x}-1}{x}}=1$?

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

Can I use the L'Hospital rule here to prove it, even though my teacher didn't teach it and my TB didn't tell me?

[hoary iris]

My book has the e^x limit in its prove therefore I am asking can I prove it using the expansion?

[hoary iris]

<@&286206848099549185>

[hoary iris]

,, \lim_{x \rightarrow \infty}{x-x}=0

[obsidian monolith]

Monkey•D•Luffy

[hoary iris]

what does this mean?

[arctic dagger]

The limit of $x-x$ as $x$ approaches infinity is $0$

[obsidian monolith]

0_א

[hoary iris]

it doesn't mean inf-inf is zero?

since x-x is zero this occurs right?

[summer ruin]

you can't split limit of sum into sum of limits, if either one of the limits doesn't exist

and in this case the limit of x as x->infinity doesn't exist

[hoary iris]

,w lim_(x -> \infty)(x-x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by kingdanger6266

[arctic dagger]

so idk. is it 0 or DNE?

,w infty-infty

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[hoary iris]

i thought x-x is already 0 which is a constant

therefore the limit is zero i thought

isn't it correct?

[arctic dagger]

idk I think i never properly learned the subtleties of limits

[hoary iris]

isn't it essential for calc?

[arctic dagger]

i guess they don't teach non essential stuff

[hoary iris]

are you doing courses other than pure math i suppose?

[arctic dagger]

no. nothing

i did. but rn I'm learning partial derivatives

[hoary iris]

ohh okk

carry on

[hoary iris]

anyone tell me about this

[willow skiff]

even simpler, $\lim_{x \to 0} \frac{x}{e^x - 1} = 1$ and now sub $x \mapsto \ln(1 + u)$

[obsidian monolith]

south

[willow skiff]

see what happens

[fading monolith]

It is

I mean, when you try to subs on the limit you have inf-inf an indeterminate form. But if you do some algebra then x-x=0 so the limit is 0

[arctic dagger]

ok i see. nice

so u can do that

should've thought of that. if ur allowed to divide variables u can also add/subtract them

[willow skiff]

so this is not equal to $\lim_{x \to \infty} (x) - \lim_{x \to \infty} (x)$ !!!

[obsidian monolith]

south

[willow skiff]

you can only split apart the limit like that

if both limits are finite

[arctic dagger]

i see

[hasty lily]

This means it equals zero

[rose birch]

is there a calculus channel and do I have to choose undergraduate math?

or does this count for calculus too

[hoary iris]

@rose birch yes there is #calculus

[rapid tartan]

How do you get a linear function from the derivative of y^2=2px? I forgot

[raven spear]

derivative of both sides

[balmy eagle]

Hi, could someone please explain to me, what is Indermediate value theorem used for?

You can prove that there is a zero in the given interval, but how is this information helpful in calculating the roots?

What about doubled zeros? Those that just touch the x axis go back

[summer ruin]

it proves that your question has a solution when you ask whether there is a root in the interval, provided the theorem holds

i. e. your problem is not unsolvable

[scarlet wyvern]

When you square root r both sides you have the plus or minus but do i base my interval off that?

sorry i kinda phrased my question weirdly but i think it's more clear in the 2nd picture

the original equation would be r^2=9sin(2theta)

[willow skiff]

X would be $[0, \pi/2] \cup [\pi, 3 \pi/2]$

[obsidian monolith]

south

[willow skiff]

first consider $r = -3 \sqrt{\sin 2 \theta}$ which traces out $X$ for $\theta \in [0, \pi/2]$

[obsidian monolith]

south

[willow skiff]

then multiplying r by -1 corresponds to a rotation of 180 degrees

so r = 3 sqrt(sin 2 theta) for theta in [pi, 3pi/2] is the other piece

[vernal path]

set notation stuff on the first page of my probability notes: what does it mean and how do i get used to reading this like how i read equations?

[summer ruin]

"all omega such that X of omega is equal to x"

[vernal path]

how does this make sense? if every omega within Omega makes X return x then is X a constant function? then whats the point of probability?

[summer ruin]

it doesn't say every omega does this

it's a set of omegas that do

[vernal path]

so its the left thats satisfying the conditions on the right

as opposed to the right side being a propoerty of the left

[summer ruin]

I don't see the difference you're making here

you can say X(omega) = x is a property of omega

[vernal path]

like

[vernal path]

"all omega" only if "X(omega) = x"

[vernal path]

X(omega) = x for all omega

[summer ruin]

$\omega \in \Omega$ doesn't mean "for all $\omega \in \Omega$"

[obsidian monolith]

Transparent Elemental

[summer ruin]

you can say X(omega) = x for some omega from capital omega

[vernal path]

oh thx

[potent marten]

say i wanna learn calculus before my calculus class in school
because why not

where could i go to do that

[elfin cargo]

KhanAcademy might be a good place to start

[brave spruce]

Online resources for self study calculus 2??

[oblique wave]

What is calculus 2?

I'm learning integration now, is that what calculus two is?

[winter comet]

calculus 2 includes the common integration techniques, calculus with parametric/polar functions, sequences and series, ect...

[oblique wave]

Ah

[vestal nest]

just a question is there any pre-university claculus channel

[blissful hill]

hey guys i have some questions on exponentials

[winter comet]

#calculus , "pre-university" and "early-university" or "undergraduate math" are just titles for the math you're doing not for your actual school status

[vestal nest]

oh thank you
it just wasn't on my channels list

[winter comet]

https://tenor.com/view/aladdin-jasmine-carpet-flying-moon-gif-22582378

[honest pulsar]

Yo I got a F in precal rn, past 2 quarters I got a D, comeback soon or nah?

[raven laurel]

does anyone know how to find the focus of a parabola

[brave spruce]

Lock in.

[weak brook]

please help me

[pine plaza]

can anyone teach me calculus

[silent prism]

I know someone like that

Very sad

[arctic meteor]

$$lim_{x \to 0} \bigg (\frac{ln(x+1)}{x}\bigg)^\frac{1}{x}$$

[obsidian monolith]

wolly5114

[arctic meteor]

the answer should be -1/2 but I get 1/2

[arctic meteor]

I used a different method

The final result is

$$\frac{x+1-e^x}{x^2}$$

[obsidian monolith]

wolly5114

[arctic meteor]

How does this equal -1/2

?

I used the limit properties of log and the exponent e

[exotic barn]

,w Limit[(ln(x+1)/x)^(1/x),x->0]

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by adoniszgks

[exotic barn]

jokes on you, both are wrong

[arctic meteor]

how do you get that answer?which part in my steps were wrong?

@exotic barn

[exotic barn]

last step it seems you forgot the 1+ you added before

[arctic meteor]

where?

[exotic barn]

last line

also what happened to the 1/x

[arctic meteor]

1/x got multiplied with that fraction

i have a method of eliminating the exponent

i don't know if this is learned in the USA

[arctic meteor]

If I get this answer do you multiply it by x+1+e^x like in the radicals?

This is what confuses me

[exotic barn]

after that idk what you did

[arctic meteor]

after that i tried to use the log property so i added 1 then subtracted 1 and I used the formula

$$lim_{x \to 0} \frac{ln(1+u(x)}{u(x)}=1$$

[obsidian monolith]

wolly5114

[exotic barn]

ln(x+1)/x goes to 1 yea

i still cant see where you are going

[arctic meteor]

where u(x) is the function

is this wrong what i did?

The limit would be like this

$$\lim_{u_x \to 0} \frac{ln(1+u(x)-1)}{u(x)-1}$$

[obsidian monolith]

wolly5114

[arctic meteor]

Is this wrong?

@exotic barn ?

[exotic barn]

no

if you do that tho you translate it

like that is goes to 1 if u_x goes to 1 now

it's like doing a sub

u(x) = v(x)+1

[arctic meteor]

In google I found this

https://www.youtube.com/watch?v=4_bemwh9q-c

Where does e^x-1^2 come from this limit?

[civic fractal]

@everyone hi friends

[willow skiff]

it's a problem solving technique

[arctic meteor]

Also how does this apply to

[willow skiff]

they manipulated the limit to get 1^2 = 4L (sub 2x = u) - 2L

where L is the limit

[arctic meteor]

$$\frac{x+1-e^x}{x^2}$$

[obsidian monolith]

wolly5114

[arctic meteor]

You use

$$(e^x-1)^2$$

[obsidian monolith]

wolly5114

[willow skiff]

oh just multiply by -1

[arctic meteor]

?

[willow skiff]

multiply (e^x - x - 1)/x^2 by -1

[civic fractal]

help please with this question

An ice cube tray of negligible mass contains 0.315kg of water at 17.7 degrees Celsius How much heat must be removed to cool the water to 0.0 degrees Celsius and freeze it?
Express your answer in joules, calories, and in Btu.

[willow skiff]

what have you tried so far?

[civic fractal]

at this point ive tried to solve it so many times i cant remeber what i tried becasue of how much it has hurt my brain

[willow skiff]

alright, Q = mc (delta T) to cool down the water to 0 degrees, and then Q = mL to turn the water into ice right?

[silent prism]

Bless l'hopital I am not tryna do allat

[fair lantern]

hello can someone please tell me how to check which parts of the graph of a cubic function are above or below the x-axis between the x-intercepts or if anyone can find a video on it thanks

[rocky wind]

in general you need to solve the cubic equation and see

for classic topics like this, i think you can search it yourself

[empty island]

can anyone find the sum of T

[fallow oasis]

Doing school project on end-users insights sort of like an interview where. https://docs.google.com/forms/d/e/1FAIpQLScGqyZVUqd6ohqK1bVYawpHwb1nddQU9krMmMakseYh6PyekA/viewform?usp=header

[arctic meteor]

$$\lim_{x \to a} \frac{x^n-a^n}{x-a}$$

[obsidian monolith]

wolly5114

[arctic meteor]

Do you replace x-a with a term?

Like

$$u=x-a$$

[obsidian monolith]

wolly5114

[arctic meteor]

I want to solve it without differentiation

[summer ruin]

binomial expansion

[arctic meteor]

i replace x-a with u?

@summer ruin ??

[summer ruin]

yes

[magic owl]

there is another way