precalculus

[sweet lintel]

how do i do this? 2 numbers have a sum of 120. time the numbers such that the product of one and the square of the other is a max.
i am thinking x plus y equal 120. idk what to do after

[fluid sorrel]

Point of intersection is hf-ag/ab-h^2 , hg-bf/ab-h^2

??

[willow skiff]

the product of one and the square of the other?

oh I see, so you want to maximise xy^2

so you can write y in terms of x, then differentiate and set to 0 and so on

or you could use AM-GM if you know it

[sweet lintel]

we didn’t learn derivative yet lol
this is pre calc
so i have 120-x equals y
what should i do after?

[willow skiff]

so you want to maximise x (120 - x)^2

[willow skiff]

do you know what AM-GM is?

[sweet lintel]

nah
i can look it up

[willow skiff]

or perhaps are you allowed to just graph it

[sweet lintel]

we can’t it’s no calculator

[willow skiff]

ask your teacher how you are supposed to do this question without AM-GM and without calculus

I think your teacher didn't teach your class well

[sweet lintel]

ok thanks

can u help me with 1 more question.

[willow skiff]

sure

[sweet lintel]

number 7

p over q doesn’t work

i tried every synthetic division using p over q

they all have a remainder

[willow skiff]

oh, search up Vieta's formulas

that tells you the sum of the roots is -(-7)/2

[sweet lintel]

😭😭😭

[willow skiff]

and the product is -(-8)/2 for a cubic

it's technically (-1)^3 * (-8)/2 but that's the same

[sweet lintel]

hopefully it won’t be on test cuz it’s the dirst time i heard that

[willow skiff]

yeah I can clearly see this now

[sweet lintel]

this is so dumb it’s not even in the textbook on the unit we have test on

[willow skiff]

wait let me check if it's factorisable

[willow skiff]

,w 2x^3 - 7x^2 + 6x - 8 roots

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

yeah definitely not

[sweet lintel]

how can we even find the roots

if we can’t find root we can’t do product or sum of roots

[willow skiff]

ok, let me show you the idea

easiest to start off with a quadratic

[fluid sorrel]

We can dude

[willow skiff]

can you expand $(x - p)(x - q)$?

[obsidian monolith]

south

[willow skiff]

where p, q are the roots

[sweet lintel]

he’s

it’s

x square minus xp minus xq plus px

idk if i said it right

should i send pic of calculation

[willow skiff]

well, $x^2 - (p + q)x + pq$

[obsidian monolith]

south

[sweet lintel]

yea

[willow skiff]

I think you just typed px wrong

[willow skiff]

yeah, so given we have this

we can do $-1 \cdot -(p + q)$ = sum of roots

[obsidian monolith]

south

[sweet lintel]

what is this formula?

[willow skiff]

so it doesn't matter that we don't know what p, q are

if it's x^2 - 8x + 15, we know the sum of roots is -1 * -8 = 8

[willow skiff]

it's a consequence of what I just said

p, q are the roots

[sweet lintel]

are the roots just p and q?

[willow skiff]

yes

[fluid sorrel]

😭

How did u jump to cubic not knowing quadratic

Ur teacher is ass

[sweet lintel]

how does this work? like what did you do then to x square minus p plis q x plus pq to get this?

[willow skiff]

their teacher didn't teach properly I bet

[willow skiff]

you just expanded (x - p)(x - q) remember

so okay, now we can compare coefficients

if $x^2 + (-p - q)x + pq = x^2 - 8x + 15$

[obsidian monolith]

south

[willow skiff]

we must have $(-p - q)x = -8x$ and $pq = 15$

[obsidian monolith]

south

[sweet lintel]

oh yea but original isn’t a quadratic

[willow skiff]

yes, it's a cubic

[fluid sorrel]

https://youtu.be/cSToB0vpgIk?feature=shared

[willow skiff]

so try expanding $(x^2 + (-p - q)x + pq)(x - r)$ for yourself

[obsidian monolith]

south

[willow skiff]

where the roots are p, q, r

[sweet lintel]

should i fully expand?

[willow skiff]

now combine like terms

so you want the coefficients of x^2, x, and the constant

[sweet lintel]

my question is a cubic tho

[sweet lintel]

what will this achieve in solving the problem?

[willow skiff]

you can do something like this, but for p, q, r

[sweet lintel]

is this the only way to solve number 7?

nothing in chapter 3 of my textbook is this hard

idk why this one is

ima email my teacher and complain 😂

[willow skiff]

that's the idea behind what I did

learning takes time, hey

[willow skiff]

this seems like a random thing to do, but actually there's logic behind it

[fluid sorrel]

It seems ur not clear with quadratic too

[sweet lintel]

i did something similar last year

like when u match things with i

like whole number plus i

equals something with whole and i

then u match it

[willow skiff]

yep!

comparing coefficients with complex numbers

so this is the same strategy, even though there are no complex numbers

[sweet lintel]

so what do i compare the cubic with?

the unfactorable cubic with no roots according to p over q

[fluid sorrel]

https://youtu.be/SMBhUbU7b7A?feature=shared

Remeber the formula

I don't think u will need the general one

Right now just go with cubic

[sweet lintel]

what is this forums called?

[willow skiff]

it's also called Vieta's formulas

[willow skiff]

you compare it with what you get after combining like terms

[fluid sorrel]

Vietas

[fluid sorrel]

Bro just let him go with veita

😅 it would be easy for him

[sweet lintel]

wait i thought about it for number 5

won’t x either be 119 or 1

since is something is squared it’s the maximum

and x plus y has to be 120

[willow skiff]

no

118 * 2^2 is already larger

[sweet lintel]

so it’s infinitely close to 120 is answe

[willow skiff]

it's actually a bit non-intuitive, that one

[sweet lintel]

i have x plus y equals 120
and x square y equals max
and y equals 120-x

i think my 2nd equation is wrong as if it equal and it is limit to infinity

[willow skiff]

it's not wrong

you just don't have a method to find the max

[sweet lintel]

so it doesn’t have a answer?

[willow skiff]

it does

okay just search up AM-GM

[sweet lintel]

can u tell me answer
my dads tryna solve it lol

but idk if he’s doing it right

i’ll just learn vieta formula for 7

[willow skiff]

,w maximise x(120-x)^2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[fluid sorrel]

It's maximum for 60 and 60

Like

To get maximum product of a number broken in 2 numbers

They have to be broken equally

Like

10

5+5

5*5 will give maximum product

[willow skiff]

wrong

[fluid sorrel]

Try 7+2

Sorry

3

[willow skiff]

that's only the case for a quadratic

[fluid sorrel]

What i know is comes from AOD

[willow skiff]

AOD?

[sweet lintel]

how’d u find what to make it equal😭😭

[fluid sorrel]

Ahh the question he asked is cubic

I see

[willow skiff]

as I told you, AM-GM

[fluid sorrel]

His paper is abt cubic

[fluid sorrel]

Application of derivatives

So i think it would be 40 and 80

[willow skiff]

true, well for a quadratic you don't need derivatives

[willow skiff]

indeed

[fluid sorrel]

Yepp by maxima

[fluid sorrel]

Bro calm down

Write x=120-y

Then put this in xy^2

Now u get cubic in y

To find maximum value

Differentiate it and make greater to 0

U will get 2 values of y

Then find x

As per situation

[sweet lintel]

what does this mean😭

[fluid sorrel]

To find the value of u such that the function attains maximum value

It's called finding maxima

U will learn this in application of derivatives

[echo sinew]

If I understood correctly from his previous messages, he hasn't been taught derivatives nor the AM-GM

[sonic loom]

bruh why trig identities lowkey hard for me

[fluid sorrel]

Ahh

[fluid sorrel]

It's easy

N related

[echo sinew]

Share a doubt on them. So that we can see why they're hard

[sonic loom]

in uhh simplifying trig identities I'm having hard time figuring out what to do first like what to look for😭😭

[echo sinew]

Send an example

Otherwise it's too vague

[sonic loom]

like uh

Cos x over 1 + sin x then + 1+sinx over cos x

[echo sinew]

Instead of over, use /

[echo sinew]

So far so good

Now expand that square of binomial in the numerator

[sonic loom]

Oh I already answered that but like idk why I'm having hard time to look for the first step

[echo sinew]

You need training, a lot of practice

That's just it

The ideas come with trying and doing

[silent forge]

is there a physics server here

[raw hill]

#old-network

[elfin zodiac]

Can anyone here help me with advanced functions?

I’m currently on the graphing part of polynomial functions.

Please ping me if you can help me out!

[uncut mulch]

just ask

@elfin zodiac

[uncut mulch]

I've lost interest in this. In the future, ideally you should clearly explain what your stuck on with an problem instead of open ended/vague questions.

[fluid sorrel]

Bro just post question ppl who know answer

[elfin zodiac]

are you good at adv functions?

[uncut mulch]

There are many here that are. Don't waste time asking if people know. Just ask the question directly and people that know will come. No specific question and they won't even look.

[elfin zodiac]

k

[queen grail]

my school still teaching math wrong 💔

[winged wigeon]

Is it not x=2

There should be a hole at x = 0

[tender mist]

Exactly what I was thinking

[zealous cypress]

what grade is that

I'm still in sophomore rn

so currently I'm still learning logarithms after learning exponents and the graphic

[fluid sorrel]

Show the question bruhhh

[fluid sorrel]

Nahh bro simplify the stuff it's correct

They r asking zeros

Not critical points

[queen grail]

pretty sure it is

[queen grail]

but it would be undefined at x = 0

[queen grail]

precalculus (it can be taken any year in high school, but u have to take algebra 2 first)

[slender kayak]

X cannot equal 0 or 3, since that would result in a denominator of zero

[fluid sorrel]

No simplify the function

It's x^2/x

So x remains in numerator

So it's zero

Not undefined

[real python]

is that desmos I see?

[queen grail]

yes the goat

[manic olive]

thanks to the lads that helped me two days ago

Got a 90% on my first precalc test

[willow skiff]

no worries mate!

[manic olive]

(an arithmetic mistake killed my perfect score)

[fluid sorrel]

Wewwwwww

[fluid sorrel]

Dammmmmmmmmm

[stray wharf]

i have desmos opened a lot but i don't know how to even use it yet, i just like spinning the cube thing

[fluid sorrel]

Ohh yeah mate the denominator can't be equal to 0.... So yaaa the answer should be A

File grievance to ur teachers

[silent plaza]

Nah, the answer should be x = 2, coz if x = 3 or x = 0, the function will go undefined, so a is the correct answer.

[manic olive]

I'm at a crossroads guys

teacher is now saying option D is correct for question 5

[willow skiff]

yes, D is indeed correct

the function is getting less steep over time

[manic olive]

💀

ok

[torn pivot]

ez

[keen frigate]

can anyone recommend me a youtube video or something similar to help me learn stuff like this question, im taking precalc and i dont even know what to look up tbh

i have a test on sunday and i havent been able to figure it out in like 2 weeks

[raw hill]

Look up trig half angle formulae

This is basically just plugging in numbers into those formulas

[keen frigate]

ooooh okok

so something like this would cover stuff i need to know for it?

[raw hill]

Probably

But something like this is probably faster done by just reading

https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/03%3A_Trigonometric_Identities_and_Equations/3.06%3A_Half_Angle_Identities

[keen frigate]

ohh thank you so much

[keen frigate]

im still so confused 😭 did i even plug it in right and how do i go about solving that

it has the formulas and the example to match but it doesnt work it out so i can see the steps

[raw hill]

What

It says that $\cos \alpha=\frac{3}{5}$, not $\alpha=\cos \frac{3}{5}$ or whatever

[obsidian monolith]

Civil Service Pigeon

[viscid thistle]

2?

[willow skiff]

wait

ah you forgot the square root on the RHS

it looked wrong but that wasn't the issue

[keen frigate]

im so lost 😭

this is the formula the website says to plug that type of problem into but idek how to plug it in

[raw hill]

You could send alpha -> alpha/2

and/or scrolled down

[keen frigate]

i dont understand what im looking at

i only rlly recognize that 3.6.3 is my type of problem

[inner hawk]

integrate log(1+cosx)

[raw hill]

Multiposted: #calculus message

@inner hawk In the future, please be considerate and delete your extra posts when someone answers you. It makes sure that helpers don't waste time double answering questions unnecessarily.

[raw hill]

the explanation or the formula?

[fluid sorrel]

Make a triangle with alpha as one angle and 3 as adjacent length and 5 as hypotenuse length and get sin and tan

[fluid sorrel]

Take 1+cosx= 2cos^2x/2

But when u go ahead with that

In one step u get logcost

If u substitute

[fluid sorrel]

So this in not elementary

U can use something like clausen theorem or stuff idk

Or just leave it

It would be possible to do this question if any specific limit was given

[vestal canopy]

This is gonna sound dumb but I haven’t been in school for that long so my math skills are mid, but on my AP pcalc test for a part of unit 1, we needed to find the 0s of a polynomial using the given factor/zero (it was like x=1 or smth) When I tried synthetic division but it had a remainder. I have to find the zeros so I can graph them; is my only choice long division? My teacher never said we would need it or even went over it. What other method is there

[willow skiff]

you probably did the synthetic division wrong then

[astral apex]

if it’s truly a zero, there should be no remainder when you do synthetic division

[vestal canopy]

Everyone else said they couldn’t do it either

[willow skiff]

you should send the question if you have it then

[vestal canopy]

Maybe the test is just wrong?

[vestal canopy]

I don’t have a pic it was on a test, I will try to find a similar one online or smth

[astral apex]

did you remember to fill in 0s for any missing terms of the polynomial?

[vestal canopy]

Yes

We even went over that before class

[willow skiff]

I guess ask your teacher how to do it

[vestal canopy]

No one finished yesterday so we have Monday to finish

[willow skiff]

see if you can catch any steps which don't make sense

oh okay

that's unfortunate

[vestal canopy]

Idk if she can give help since it’s a test

[willow skiff]

yeah I didn't know your test was extended

[vestal canopy]

I’ll try to find a similar problem after I’m done eating

[willow skiff]

sure

[vestal canopy]

I’m hoping I can find out how bc it was like a 10 part problem worth 10 points, and a few of the parts are reliant on my answer

[vestal canopy]

It wouldn’t be the first time she’s messed up a worksheet

[vestal canopy]

Ik chat gpt isn’t allowed but i used it to reverse engineer the question from what I remembered. The problem the test gave me was x^3 + 6x^2 + 32 with x=2 as a factor. Apparently that polynomial does not actually have any factor (that is an integer) that will result in no remainder. I’m pretty sure the test was supposed to be -32 instead of positive, because in that case, x=2 would be a zero.

So the problem was written incorrectly

I’ll just ask the teacher if I should fix it to a negative

[cosmic leaf]

wheres the question

[astral apex]

if x = 2 is a zero, then (x-2) is the corresponding factor

[vestal canopy]

Yes

I said x=2 bc that’s the number you put next to the synthetic division thing, as well as being what the problem itself said

[vestal canopy]

Part A was x^3 + 6x^2 + 32 with x=2 being a zero. You’re supposed to use synthetic division to find the other 0s

[astral apex]

fair enough. Unfortunately it’s hard to say if the test had a typo or if you’re misremembering something

[vestal canopy]

I mean, I retried the problem over 6 times and kept getting a remainder. So unless I was just out of it that day and made the same mistake 6 times that I’m not making anymore, that was the polynomial

[astral apex]

but you said you reverse engineered it from what you remember

if you’re positive that’s what it was, then yeah x = 2 is not a zero

[vestal canopy]

I remembered all the numbers at the top of the synthetic division box

And I tried it 6 times so unless I looked over a sign 6 times idk

I guess I’ll know when I look back at it on Monday

[vestal canopy]

And remembered the exponents bc I needed a placeholder

[ivory fractal]

How do i do question 7a?

Do i need to know the function of the graph to solve this

[astral apex]

no

f(-2) is notation for the y value on the curve going with x = -2

you just look at the graph

[teal shuttle]

i have a test on monday over rational expressions on dividing and multiplying i learned it last year but idk why it’s not clicking in my brain i dont understand anything

i’ve watched youtube videos and don’t understand it

help me please

[astral apex]

are you comfortable with factoring?

or maybe comfortable is asking too much

could you factor the polynomials in that expression?

[teal shuttle]

yes

[astral apex]

nice

[teal shuttle]

sometimes it takes me long to figure sometimes

[astral apex]

factor them, and then look for matching chunks in the top and bottom that you can cancel out

[teal shuttle]

thanks

i don’t understand what i’m doing wrong

😔

[astral apex]

looks like you lost an x^2 from the top-right

also you forgot to cancel out the (x+8) from the bottom

also you shouldn't have an equal sign between your fractions

oh my mistake. Your (x+8) in the bottom is right

[ivory fractal]

thanks very much sir

[vestal canopy]

f(x) is the function, so f(-2) means the x coordinate is -2. It's asking you for the y value when x = -2. f(x) is just the technical way of saying Y when concerning functions.

and you just look at the graph below to see that the y coordinate is at 0 when x is at -2

bc it's (-2, 0)

[limber sapphire]

Precalculus bridges Algebra II and Calculus by deepening foundational concepts and introducing new topics, particularly functions (linear, polynomial, exponential, logarithmic, trigonometric) and trigonometry (unit circle, identities, graphing functions). It also covers complex numbers, analytic geometry (graphs, distance, midpoint), and algebraic manipulations like solving equations and inequalities. The core goal is to provide a comprehensive mathematical toolkit for success in Calculus.

[muted ore]

Factorize all the polynomials. Once done, please use the method of taking out common factors and multiplying algebraic fractions.

[muted ore]

Calculus is basically a topic on everything you've learned so far in Mathematics for the rest of your life. It mainly requires almost all topics (especially algebra and trigo basics) to master in order to understand the fundamentals in Calculus.

[past isle]

Someone help me with this question.

I'm class 12th student, our teacher gave this problem, I know I need to satisfy condition for continuity LHL = RHL = h(0) . But I'm not sure where to start and how to solve this demonic series. I don't know any continuity theorem or differentiation or integration, as our teacher hadn't taught those yet and gave this problem. I just know the basics and definition. I'm able to solve the limits but without using L-Hospital rule, we solve them by manipulations, identities, series expansion, standard limits.

Any help is appreciated, although if someone can solve it along with detailed step by step explanation, that would help tremendously as I was unable to get help from chatgpt or Google regarding this and I prefer written solution. However, if you just give the idea, that would also be helpful, I'll try that myself.

[sonic loom]

just finished trignometry identities its lowkey easy whats next to this topic (im grade 9)

[ivory fractal]

thanks so much

[fluid sorrel]

Graphs

[raw hill]

Reposted here: #1419374622046163125 message

[willow skiff]

<@&268886789983436800>

oh wait, I should have sent a msg to ModMail

[drowsy vessel]

Nah perfectly good to ping mods here

[willow skiff]

thanks!

[storm shuttle]

grade 9 and 10 trigonometry was sooooo easy i kinda wanna go back to that now

[sonic loom]

Oh yuhh it's just basic im studying trig identities right now I'm still confused how half angle identities work smh

[storm shuttle]

they are just like using 2x=y in the double angle formaulas

formulas(

[storm shuttle]

do infinities come under pre calc?

(i dont think so)

(i am saying this cause they have a lotta functions associated with them)

[astral apex]

depends on what you mean

asymptotes show up

and limits

infinities are studied in many different contexts and subjects; precalc gives a tiny taste of it

[storm shuttle]

isnt this false??

oh nvm

i am dumb

keep confusing b/w injection and surjection

[storm shuttle]

alr here is a stoopid proof that is very obviously wrong and i wanna know where is went wrong:
-1^infinity=P
-1*-1^infinity=P
-P=P
2P=0
P=0

...

the splitting feels wrong

[astral apex]

it goes wrong right at the start - you can't say (-1)^infinity is a number and start doing algebra with it

that kind of thing sometimes works, but it always has to have some kind of rigorous justification behind it. In this case, it doesn't work; (-1)^infinity doesn't converge in any sense

[narrow pumice]

Hi guys, who needs help with with homework for a small fee (;

[astral apex]

you can’t advertise like that here

[analog flower]

https://tenor.com/view/we-dont-do-that-here-black-panther-tchalla-bruce-gif-16558003

[narrow pumice]

But I can help you with all your assignment. I will explain in the way that you will able do it later all of you assignments by yourself and pass all exams. I am really good at math and I know small tricks that help make big problems easier!

[analog flower]

you just made your account and have no history or testimonials. why in the world would anyone send you money when they could open a help channel here instead?

[hazy chasm]

Me when

Somebory help and exprain

Please

[unborn dagger]

Oh no that’s scary, I’m still in the very basics of precal and I’m so lost 😭

And it’s literally js long division and synthetic division with polynomials or something 🤧

[hazy chasm]

Poor soul

Shes lost

[fervent elk]

me to bro liek what is that

[undone pumice]

oop gl u two my class is testing unit 1 (of ap preaclc, out of 5) in two days

[wispy musk]

https://tenor.com/view/wow-gif-15939497589680687855

im cooked

[cursive marlin]

how'd you get that app or drawing platform ive been looking for one

[rare thunder]

Hi could someone help me understand functions? I'm not exactly sure if it's precalculus or algebra though.

[frigid moat]

i think to find p if possible you do: x→0−lim​h(x)=x→0+lim​h(x)=h(0)=p⇒p=2 (I could be wrong tho ) bc im not allowed to use chatGPT as well 😭

[surreal jungle]

algebra is also in calculus???

[viscid thistle]

this ain't the 90s twin ppl js use free chat gpt if they don't understand

[astral apex]

algebra is in everything

[willow skiff]

and so is coordinate geometry

calculus is really just using algebraic and geometric techniques to observe how functions change

[fluid sorrel]

What's the answer??

Bcz i think just equate the limits

LH limit= RH limit = f(x) that's p

Take limx-> 0

[hazy chasm]

Yea duh

[true turret]

guys where is the calc channel :((

[echo sinew]

#calculus here

[narrow pumice]

I am happy for you if your gpt always gives you right answers and solves problems with the school or university program way))

[viscid thistle]

hahahahaha welcome to hell

[cosmic leaf]

lol

[wispy musk]

how do i solve this

[astral apex]

have you tried anything on part (1)?

also this is calculus, but okay

[thorny moth]

Have you calculated the derivative yet?

[forest hawk]

opinions on this abomination?

i already fixed the first statement but im sure it's trivial to figure out what i substituted it for

[true turret]

yeah had to change my role thank u!

[thorny moth]

Will I be cooked if I double down on algebra 2 & precalc at the same time

[undone pumice]

meh in my experience precalc starts with some beefed up alg2

concavity, limit statements

i think u will be fine

[thorny moth]

Alr thx

[undone pumice]

np glgl if u do decide that!

might be slightly different depending on the class, im in ap precalc and we follow the general ap unit structure (5 units)

[dusty palm]

i narrowed it down to D and E however im not sure which is 'more wrong' or im just slow idk

[thorny moth]

It’s D which is wrong, denominator should be x-3

Otherwise D will approach 0 not the derivative

E is correct since it’s like C but instead being applied to both terms of f(3+-h), which is made up with the 2h denominator

[dusty palm]

i see, thank you

[strong tartan]

If ax + b = 15 and 15x + a = b have the same unique solution, where a and b are
positive integers both less than or equal to 30, find the sum of all possible values of a.

I tried to solve this by solving each equation for x and then setting them equal to one another. I then got a quadratic in a which I used to get a formula for a in terms of b. After that, I considered all b between 1 and 30 (inclusive) which gave a value of a between 1 and 30 (inclusive) and which was an integer. When I added the resulting a together I got 120, but that answer is incorrect. I checked the numbers I got and they dont all solve the original two equations.

I guess I just want to understand why this method doesnt work. Should I be getting a formula for b in terms of a and considering all valid a? It seems like I should get all valid a for free by finding all valid b. Is it something to do with the quadratic formula?

[raw hill]

,w (15-b)/a = (b-a)/15, b=19

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[raw hill]

@strong tartan ? not every value of b gives an integer a

[fluid sorrel]

A B C E are right while D should have x-3 in denominator to make the limit valid

[fluid sorrel]

Take dt to RHS then integrate both side to get a differential equation then solve accordingly

[summer violet]

Question: when there are ‘equal roots’ does it mean that the discriminant has 1 real root?

Nvm but

[willow skiff]

it says right there that b^2 - 4ac = 0

[summer violet]

Yh I looked at that after asking

[quick jungle]

Could someone help me understand end behavior, polynomials long division, and optimizations word problems

[willow skiff]

https://www.youtube.com/watch?v=a5x4lwnvHM0&pp=ygUcZW5kIGJlaGF2aW91ciBvcmcgY2hlbSB0dXRvcg%3D%3D

if you ask for topic videos you'll always get something like this

when you could have just searched for it yourself

[nimble ridge]

organic chemistry teacher

wow

[static harbor]

yes, we say equal root, because quadratics usually have 2 roots, but when discriminant is 0 then those two values coincides, so two equal roots means one real roots because complex roots always occur in pair

[static harbor]

which software do you use?

[thorny moth]

Desmos

[latent lynx]

anyone have a good book about limits and continuite ?

[atomic junco]

what do you aim to do after complete reading the book

[latent lynx]

solving high school limits

[atomic junco]

Amit Agarwal(Arihant) The topic is in the book: differential calculus. good problem set too.

[compact egret]

precalculus when they give me something hard

i actually cant understand what you are saying guys

im sorry

[oblique verge]

Can anyone help me with computing numbers that approach infinity

(limits)

@everyone

[astral apex]

could you show the problem you’re on?

[oblique verge]

$\lim\limits_{x\to\infty}\frac{1}{x}$

@astral apex

[obsidian monolith]

𝓢𝓽𝓻𝓪𝔀𝓫𝓮𝓻𝓻𝓲

[oblique verge]

I want to understand this in a more general form, though.

If you don't mind

[astral apex]

in your class are you expected to be able to prove what the answer to that is using rigorous math (like epsilon-delta stuff) or are you allowed to have a tool belt of basic ones that you understand and can freely use without proof?

because that’s a very common / basic one that in many classes you can just say the answer

[oblique verge]

I am expected to know real anal already

yes

I am a middle schooler drop out

so no college

nor high school

or whatever

[astral apex]

how is it you’re expected to know real analysis? what’s the context here?

[oblique verge]

By myself

my friends have learned arithmetic geometry already

and they are from 9 to 14

I am 15

[astral apex]

that seems very unlikely and hard to believe

[oblique verge]

i know

one of them is a genuine asshole sometimes

[astral apex]

are you sure you don’t mean analytic geometry? Like the distance formula and graphing in the xy-plane?

[oblique verge]

No.

[astral apex]

arithmetic geometry is a PhD level research area

[oblique verge]

Yes.

and I want to get there before I turn 18

I just started calc like 6 months ago

7*

took a 3-month-long break

started math overall

cuz I really never bothered to learn outside of school

we have a server

if you want to factcheck

I mean

the rules are there

but I want to understand what's going on

[astral apex]

I believe you, but realistically what you desire is not possible. I take it your friends for some reason had the luxury of having an extraordinarily rare math upbringing

[oblique verge]

yk?

[oblique verge]

we'll see

We will see...

I am currently learning about series

[astral apex]

keep learning math by all means

but that timeline for the amount you have to learn is ridiculous

[oblique verge]

That aside, can you help me with my question?

[astral apex]

sure

as x gets big, 1/x gets small. Always positive, toward 0

[oblique verge]

but some aren't as obvious at first glance

[astral apex]

and that fact can give the answer to an infinite limit of any rational function

[oblique verge]

I see

[astral apex]

but other functions will require other approaches

[oblique verge]

I am learning about geometric sequences, and since I saw something that stated that |r| should be less than 1

when I tried to compute it raw, I got stuck with the infinite limit

I will show you the function

This limit diverges, btw

just looking for an explanation

$6 \cdot \lim\limits_{k\to\infty} (1-(\tfrac{4}{3})^{k+1})$

[astral apex]

ok

do you agree that using limit laws, we can reduce that to figuring out the limit for (4/3)^(k+1) ?

[oblique verge]

yes

[obsidian monolith]

𝓢𝓽𝓻𝓪𝔀𝓫𝓮𝓻𝓻𝓲

[oblique verge]

thanks for helping me, btw

I see you are helping various at a time

It's diverging, so sorry

not non-existent

[astral apex]

no worries, happy to help

[oblique verge]

😓

[astral apex]

you can break that up further

the limit of 1, constant, is just 1

[oblique verge]

yeah, sure

[astral apex]

and you can pull the negative out

[oblique verge]

$6 \cdot (1 + \lim\limits_{k\to\infty} ((\tfrac{4}{3})^{k+1}))$

[obsidian monolith]

𝓢𝓽𝓻𝓪𝔀𝓫𝓮𝓻𝓻𝓲

[astral apex]

okay, so we want to show lim k->infty (4/3)^k is infinity

or k+1. That doesn’t change anything

[oblique verge]

would a table of values suffice it?

[astral apex]

no

it can give you confidence that that’s really the answer, but it won’t prove anything

we need the definition for what it means for an infinite limit to have an answer of infinity

[oblique verge]

yes, i like that

[astral apex]

lim k-> infty f(k) = infty means: “For any M > 0, there exists an x in R for which k > x implies f(k) > M”

that is, if a value for the function is chosen, then if we let k get big enough, we will exceed that value forever

[oblique verge]

what x?

[astral apex]

that depends on the function and chosen M value

[oblique verge]

okay

yeah

ik

[astral apex]

so in our case

[oblique verge]

it's just that why is it k>x? is it because of the k+1

[astral apex]

oh, I switched from k+1 in the exponent to k. That makes no difference for the answer

as long as the exponent is going to infinity, the answer will be the same

[oblique verge]

I don't get what x has to do with all this...

[astral apex]

we have to demonstrate that there exists such an x for any M

it is the number that controls the meaning of k being “big enough”

[oblique verge]

yeah, I get that f(x) will be always smaller f(k) as k gets bigger, thus f(x) < f(k)

It just seemed so "pulled out of nowhere"

I still have a lot to learn

[astral apex]

that is true here (because this f is a monotone increasing function), but it’s not really the point of the x being brought up in the definition

the point of that x is it has the property f(k) > M for k > x

[oblique verge]

yeah... x is just a real number that adds to the fact that k will always be bigger than x no matter what!

[astral apex]

anyway

consider (4/3)^(k+1) and a chosen number M > 0

[oblique verge]

just a formal definition, omg

[astral apex]

how big does k need to be to guarantee (4/3)^(k+1) > M ?

[oblique verge]

k >= 0

[astral apex]

that does not guarantee that

what if M is 1000000?

[oblique verge]

i see

well, k can't be real number in that case

so I'd say something like infinity

Wait

no

k has to be more than M

that's it

[astral apex]

we need to find a finite x for which k > x ensures f(k) > M

[oblique verge]

oh

[astral apex]

do you have a proof this works?

[oblique verge]

no

[astral apex]

well, maybe it does. The idea is maybe we can take x = M

[oblique verge]

oh gosh

[astral apex]

it’s possible that works, but needs to be checked

[oblique verge]

is this what analysis looks like

[astral apex]

yup!

I think using x = M doesnt work for all cases here

but it works for large enough M

it’s a good thing to think about. But usually to solve these problems and find x, it involves working with your function’s expression in some way

[oblique verge]

it does

I will find all the possible solutions

Can you clarify what M means?

Is it the output of the limit?

[astral apex]

its a finite positive number allowed to be freely chosen, and when the choice is made, we have to demonstrate f(k) can be larger than that

like, we’re wanting to show the limit at infinity of f is infinity

so that entails showing it eventually is bigger than 100, 1000, 6352749, etc

all of those are potential choices of M

kind of like how epsilon is a freely chosen “error tolerance” in the other limit definition

M is a freely chosen sort of height benchmark

[oblique verge]

@astral apex, x can be any real number

[astral apex]

yes

[oblique verge]

you said that already, though

[astral apex]

for a particular choice of f and M, not just any x will work

but in general x could be any real number

[oblique verge]

x = M won't work when M > infinity

...

[astral apex]

x will be found in terms of the constant M and the given function f

M is finite

[oblique verge]

I need help, I don't get it

[astral apex]

ok. This stuff is notoriously challenging so no worries. But let’s move this to a more appropriate channel

do you have access to #real-complex-analysis ?

or #calculus should be fine

[oblique verge]

sure

[astral apex]

cool

[supple karma]

i need help with piecewise functions

[fluid sorrel]

It's correct

The point of intersection of graph of parabola on axis depending upon it's orientation indicates the number of roots

[modest bolt]

Can you show any questions you are having trouble with?

[oblique verge]

okay

[vestal canopy]

I did not expect to do good 🙏 I switched to AP so I only had 1 day of class to learn all of the material

[oblique verge]

Okay?

How old are you?

I have never seen AP pre-calculus!

[viscid zodiac]

Maybe it's AB? Then BC is their calculus course?

[frank timber]

AP precalc is a thing now

https://apstudents.collegeboard.org/courses/ap-precalculus

idk since when tho

oh yeah like 3 years ago

[vestal canopy]

It’s new I think collegeboard made it in 2023

Or 2022

[oblique verge]

oh okay

[forest dirge]

can anyone pretty please provide a step by step lessons i need to master or have proper knowledge in to be able to proced in learning pre-calculus and even calculus?

[uncut mulch]

khan academy has free structured courses

[forest dirge]

ohh, thank youuu

ill look at it

[vestal canopy]

khan academy and search for an algebra 2 lesson playlist on youtube (assuming you know basic algebra 1 and pre-algebra) some schools let you take calculus after getting a good grasp on algebra 2 (though the traditional path is algebra 2 > pre-calc > calc), so thats what im basing it on. I havent taken calculus yet so i can't go that deep into what skills you'll need. Im in Precalc

[forest dirge]

ooohh thank you veryy muchh

[dusk knoll]

in which year would you usually reach calculus 1?

[quick jungle]

11th grade

[willow skiff]

there's a huge variance in maths ability though

some people get there at 13; some people never get there and have zero use for it

[dusk knoll]

okayy thanks!

[willow skiff]

this is when it's taught to students, I agree

on average (the world is a messy and diverse place)

[quick jungle]

Ye im taking precalc rn

Im in 10th grade

I think we do ap calc ab or smth next year

I have forgotten tho

[willow skiff]

cool

[dusk knoll]

I think I finished precalc halfway through 10th grade or earlier

[odd heath]

Khan academy and youtubers like the chemistry tutor guy

[hybrid stratus]

yo who wanna help me wioth an exam i got in3 hours

🙂

[undone pumice]

yeah prolly, i take calc ab in 10th

or bc if i skip but prolly not...

[low rose]

hi

anyone know what matrices are actually used for?

or matrix

Im doing them rn in precalc and understand them, but what are they used for

[undone pumice]

they can be used to represent linear equations and solve for systems of equations (gaussian elimination)

or transformations on a plane

adjacency matrices are used in graph theory

[low rose]

ahh I see

Ty

[willow skiff]

yes, that's the algebraic motivation above for matrices

geometrically, matrices are about rotating and scaling the coordinate plane

[low rose]

lowkey there easy for me for now

[low rose]

Ohh

[willow skiff]

https://www.3blue1brown.com/topics/linear-algebra

a vector after all, is just an arrow in some coordinate space right?

and any line, say 2x - y = 3, can of course be represented geometrically

[tender mist]

Meanwhile there's that one 11 year old kid doing integral calc on YT, lmao. People of crazy skill levels all over the place

[willow skiff]

oh right, Goh Pi Han

totally forgot they existed

[tender mist]

I briefly saw a video recommended, never ended up watching it, but yeah, that probably sounds right

[north pecan]

hi guys

[willow bear]

#chill

[mortal folio]

Guys can anyone help me in burnside lemma and group theory

I am just flabergasted by burnside lemma

[hushed sphinx]

That's #groups-rings-fields material.

[fluid sorrel]

Wowwwww

Crazy

[rough jolt]

One use is in algorithms and such im pretty sure

Like machine learning

[low rose]

ahh

[rough jolt]

Also are used in physics

For circuts or smth like that

[low rose]

also do you know the difference in future careers between pure math and applied math?

[rough jolt]

Im in applied math

So yeah i cn kinda speak

I think end of the day both r just degrees

Applied math gas more use

Because u can spread ur knowledge into finance or tech

[low rose]

I see

[rough jolt]

But if u took pure math and learned to code and read some finance books or smth u could get a career

[low rose]

But I’m guessing pure math is just classes filled with math and applied math has lots of math but other courses depending on ur future career?

[rough jolt]

My uni u take stats, linear regression, etc etc which have applications in operations research, data jobs, investment banking etc

[low rose]

I see

[rough jolt]

Pure math just specialize in analysis or topology or etc

[low rose]

I wanna be a data scientist, so what would my courses look like. (Apart from math)

If you know

[rough jolt]

End of the day if u learn to code and u have good networking skills yu’ll be fine

[low rose]

So let’s say the career I want involved a bit of coding

Would I take that in uni

[rough jolt]

Hmmm intro to python, R, data structures n algorithms, maybe more emphasis on stats

[low rose]

I see

And that would correlate with all of the math courses right

[rough jolt]

Wdym

[low rose]

I mean like I would take them at the same time

[rough jolt]

you can

[low rose]

Like one period is math then the next might be coding and then again math etc

[rough jolt]

for me

im trying to go into data as well

but im not really taking any classes tbh lmaoo

[low rose]

How does it work tho? Do you tell them like what you wanna be and then they recommend he courses to you

[low rose]

Ohhh nice

[rough jolt]

im just learning python for fun and then move on more

u can learn a lot from yt btw

free resource the hardest part of data science is the math from what people have told me

[low rose]

Ohhh

For college do you choose your courses or do they recommend your path based on what you wanna be

[rough jolt]

if you can finish with a degree in math it’ll show employers that you are intellectual, work hard, etc. but it also shows that u have the math for data

[rough jolt]

so im jn canada so i cant speak for your country

but for me

we had core classes

so my first year i HAD to take calc 1&2, intro to proofs, linear algebra, stats, and then i had some electivrs

so i took chemistry 1 and 2

[honest juniper]

man i hate proofs

[rough jolt]

but yeah you’ll most likely have some mandatory classes you’ll need to take

for your major

[low rose]

Ahh I see

[rough jolt]

if you go into applied math you’ll be taking less proof classes

more computation and applicable

[low rose]

Yeha proof is more pure math

[rough jolt]

to the real world

[rough jolt]

my uni i’m still required to take real analysis

but yeah

so you have to take the basic math classes

but tbh those are good for dats science

[low rose]

I see

[rough jolt]

i feel like 1 linear algebra course calc 1,2 and 3 and stats 1 and 2 should be sufficent for data science

but u learn a lot in uni

[low rose]

Yeah

Do they recommend clases?

[rough jolt]

dont be afraid to take classes that interest you

[rough jolt]

sometimes yeah if u ask

[low rose]

Yeah ofc

but otherwise you choose it yourself right

[rough jolt]

my department head told me i should take python

i’m gonna take it next semester

[rough jolt]

yeah

[low rose]

Ohh nide

Nice*

[rough jolt]

if u dont mind me asking r u going to uni next year?

honestly if you are maybe talk to guidance counsellor at your highschool they should also be able to help

[low rose]

Nah Im a sophomore, so another 2 years

[rough jolt]

maybe find math majors on linkeden and talk to them?

like math alumni

who graduated

[low rose]

Yeah that’s also a good idea

[rough jolt]

find a math prof at a nearby uni n email them some questions

[low rose]

Would they respond?

[rough jolt]

maybe email the math department

[low rose]

Like generally

[rough jolt]

idk but its worth a shot

i didnt ever do it

but you have nothing to lsoe

lose

[low rose]

yeah it’s just that I don’t wanna take the wrong classes in college

[rough jolt]

yeah you’ll be fine

if you find your uni of choice

search up their applied/pure math program

and see the mandatory classes

[low rose]

Oh wait that’s smart

[rough jolt]

also check their computer science department and the classes for those

[low rose]

I forgot to think about that lol

[low rose]

Yeah

[rough jolt]

and plan out which cs classes to take and which math

[low rose]

I’ve heard many of the applied math future careers require some kind of programming

[rough jolt]

yeah typically they do

[low rose]

not as extensive as being a cs major obviously but it’s there

[rough jolt]

thats why you’re lucky ur still in hs

learn programming now

[low rose]

lol yeah

[rough jolt]

while u have the time

[low rose]

I’m learning python rn

[rough jolt]

thats amazing

i personally struggle with coding

i hate it

[low rose]

It gets a bit hard yeah

[rough jolt]

but yeah if u can get good at that

you’ll be good

[low rose]

Yeah

Thanks bro for the help

[rough jolt]

no problemo

also go on reddit n search up applied math + the uni of your choice

thats what i did

to hear how the program was from legit students at that school

[low rose]

Ahhh I see

Thanks a lot

Really helpful

[low rose]

when do you use mean of a population vs mean of a sample

i dont get it

[viscid thistle]

Calc is short for calculator

I know because I am an expert on calcs

[willow bear]

you're also at least half wrong

[topaz tinsel]

Uh is this precalculus?

[willow bear]

looks very much like calculus calculus

[fluid sorrel]

Integral calculus

Mid part looks like greatest integer function

[mighty bramble]

i have heard of calculus before but i do not know what it is

[jagged compass]

Fun Question try this:
[
\text{ If } \alpha = e^{\frac{2\pi i}{11}} \text{ and }
f(x) = 5 + \sum_{k=1}^{60} A_k x^k,
\text{ then find the value of }
\frac{1}{11} \sum_{r=0}^{10} f(\alpha^r x).
]

[obsidian monolith]

TheSup_3912

[wispy widget]

Guys can anyone tell, why area under the curve is the opposite of derivative, i mean i know integral is defined as antiderivative but why does the area under the curve is inverse operation of rate of change?

[hushed sphinx]

That's definitely #calculus rather than PRE-calculus.
It's not all that common to define integrals as antiderivatives nowadays (though that idea has some historical pedigree back to Leibniz and Newton).
What's actually true (with modern definitions) is the Fundamental Theorem of Calculus (look that up!) and the operations are no more and no less "inverses" than what that theorem says. The duality is occasionally rather oversold in non-technical presentations, but don't take it for more than it is.

[jagged compass]

https://youtu.be/FnJqaIESC2s?si=YfCzin2U8hNcNsSw

https://youtu.be/rfG8ce4nNh0?si=weDWVxAH-yomVv8B

Two perfect videos explaining exactly that

[soft plover]

what is A?

[jagged compass]

Nth term of an arbitrary sequence

[soft plover]

then the answer would contain A?

cuz it's unknown

[median spear]

See, integration can be understood as joining each and every bit of a broken piece, whereas considering differentiation as breaking apart smtg in small ones. So to calculate the area u need to sum up. The rate of change is whereas finding change happens to the smallest part(lim~0).

[wispy widget]

Your answer doesn't match my question 😂

[median spear]

Fine

[honest juniper]

3blue1brown is so goated dude

[modern mortar]

What’s precalculus?

Idk the difference between calculus, algebra and precalculus

[red mason]

Algebra is about solving equations with numbers and variables
and precalc is just that but with functions, graphs, and trigonometry
its just a bridge to actual calculus with derivatives and what not

[modern mortar]

Ok ok ok, ty

[topaz tinsel]

Thx there’s no way I just realized that lmao.

[undone pumice]

lwk idk if this is in this channel or not

but i only have the pre-uni roles

so

could someone help with this?

i dont get how to find it

and im not supposed to use l'hopital i think

and idk how else to solve for indeterminate form without like identies or sum

[river drift]

this is a famous limit that you're generally expected to just know. the usual proof is with geometry and the squeeze theorem, for example in this video: https://youtube.com/watch?v=5xitzTutKqM

[wispy widget]

All are same some, fuckers think that they are different entities but they are actually same

[river drift]

often it's considered famous enough that you can use it without proof in other problems

[undone pumice]

ohh okay

i dont need to prove it but like

its being used somewhere and i like

dont get why thats true

so like i js need to get my dumbazz to understand it

[wispy widget]

do it by graph , there's no other way to solve this, as this limit is the basic limit , you use this to solve higher limits, think it as , can you prove 1+1=2?

[undone pumice]

oh

[river drift]

you can prove it, the proof is in the video above

[jagged compass]

Use the squeeze theorem

[undone pumice]

k

[jagged compass]

Here is a solution:

I have Good question, try this chat:

$$
\textbf{Find the domain of the function }

f(x) ;=; \log_{\lfloor x + \tfrac{1}{x} \rfloor} , \big|x^{2} - x - 6\big|
;+; {^{16-x}}C_{2x-1}
;+; {^{20-3x}}P_{2x-5}
$$

[obsidian monolith]

TheSup_3912
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[jagged compass]

Yes try this guys

[fluid sorrel]

Calm down girl they r different

[wispy widget]

Complex numbers require integration at higher levels, that means arithmetic and calculus are same

[fluid sorrel]

Agree with the first part but complex numbers behave as vector entities so they r highly geometry based

[wispy widget]

Some dumbos think vectors are part of calculus and some think they are part of algebra z what about that

And you think they are part of geometry

[fluid sorrel]

It's a combo

But mostly geometry

[jagged compass]

Vectors are found everywhere in higher maths, so they are not exclusively part of anything, they are found in lots of fields

[fluid sorrel]

With help of algebra tools

[jagged compass]

*linear algebra

[fluid sorrel]

Yeah

[median spear]

One of the simplest methods would be using sinx expansion.

[median spear]

Wth , there are differences

[rugged sleet]

Start off by defining C and P

C(n,r) is defined if 0=<r=<n

C and P domain should limit x to a great extent.

C domains gives you 0.5=<x=<17/3

Guess: ||Domain might be empty||

[jagged compass]

Nope,
calculate domains separately for the absolute value part, the C, the P and the floor function. And the domain of the function is just the intersection of all those

[jagged compass]

One more hint is that n=>1 and r=>0 for both C and P

And the base and the input of the log can never be zero

[rugged sleet]

I made a rough guess that the intersection of domains of C,P, floor and all would be empty. Might not be the case.

[keen smelt]

anyone know how to solve this question

[raw hill]

In the future, please do not cross-post questions across channels - it can lead to multiple of us answering the same question, which is an inconsiderate waste of our time. Also, please show what you've done so far in the future when asking for help.

There are two (and a half) ways I can think of going about this. The first is to recall that the powers of i cycle every four, so compute the terms in groups of 4 and notice the pattern. Alternatively, you can interpret this as an arithmetic-geometric series and follow the standard algorithm (||let the sum be S, then compute Si and subtract||). The two and a half'th way is to write this in terms of a reindexing argument instead.

[keen smelt]

thank you so much sorry im new i didnt know about that before

but does anyone know how to get the end product of this

[raw hill]

There are two (and a half) ways I can think of going about this. The first is to recall that the powers of i cycle every four, so compute the terms in groups of 4 and notice the pattern. Alternatively, you can interpret this as an arithmetic-geometric series and follow the standard algorithm (let the sum be S, then compute Si and subtract). The two and a half'th way is to write this in terms of a reindexing argument instead.

I gave you multiple ways to compute the sum

[keen smelt]

im sorry i understand the first method and notice a pattern however was unsure how the answer came to the rcis form having these number

[raw hill]

So you already computed the sum in rectangular form?

[keen smelt]

i think so i coimputed the sum with n=1, n=5 n=9 and the common pattern is 2-2i i am unsure where to go from here

[raw hill]

Well

How many groups of four are there

[keen smelt]

would be 505 right given the maximum of the sum is 2020

[raw hill]

Yes

So what is the overall sum

[keen smelt]

?sorry im confused

like to get it intro rcistheta form

[raw hill]

Stop focusing on the final goal

You need a definitive answer in rectangular form to convert it polar form

You don’t have a definitive answer in rectangular form

Which is what I’m asking you to find

[keen smelt]

505(2-2i)

[raw hill]

Mhm

Or 1010-1010i

Now you can follow the standard algorithm to convert this to polar form

[keen smelt]

oh

thank you so much civil service pigeon

i really appreicate it

[ripe eagle]

jw would you tutor?

[raw hill]

no because this is something I use to fill the (irregular) gaps in my day

[ripe eagle]

ur okay thanks for the response 👍

[fluid sorrel]

Which class are you

[patent barn]

What is this gibberish? Y’all know what it means?

[vagrant lichen]

aggggh

I’m so pissed bro

I always ace them fricking regular math equations

but then I fumble word equations bro

what is wrong with me

[viscid thistle]

Yeah

[chrome acorn]

an altier couldve been by using the expansions of sinx and then observing whuch terms are remaining and which tend to zero...

[ripe eagle]

i’m in accel pre calc

[fluid sorrel]

I mean what level ru studying

Grade?

Your level

[median spear]

Exactly, that's the easiest way to do it to me too!

[undone pumice]

gng does anyone mind answering a calc question cus i selected pre uni math and apparentely that doesn't have a calc channel

lwk ion get the chain rule

[odd ocean]

just use chain rule

[undone pumice]

Um what’s the chain rule again

[fringe acorn]

is it D?

[median spear]

Ok chain rule, first take derivative of cos followed by exponential function

Js think about it as , differentiating outer brackets and simply moving inside . Js every time u do so, multiply the derivative

Eg. -sin(e^x) e^x

First take the derivative of the cos , now it's angle is also a function of x , so differentiate it again too!

[undone pumice]

Ohh ok thank you!

[median spear]

Always

[long lynx]

Can someone help me understand the derivatives definition 🙏

[halcyon prawn]

Think of it as local approximability via a linear (possibly affine) map

[long lynx]

could you elaborate

and possibly explain using easier to understand words 😭

[hallow ermine]

Im sure there are many videos which can help you with that

[undone pumice]

the limit definition of a derivative?

[wispy widget]

In simple words , it is infinitely small increase in y variable divided by infinitely small increase in x variable , or the slope of tangent at a point to a curve

[fluid sorrel]

Slope of any curve or the point where the LHL and RHL become equal

[odd ocean]

divided by?

[odd ocean]

f’(a) is the unique slope L such that the affine map A(x) = f(a) + L(x-a) approximates f near a with the approximation error vanishing faster than the distance from a.​​​​​​​​​​​​​ itself

[wispy widget]

Yupp

[wispy widget]

Stop trying to understand such complex definitions, derivative is a basic thing

Simple

dy divided by dx

Where dy or dx is an infinitesimal change

[wispy widget]

That's a half definition of continuity not derivatives

[hard sluice]

Does anyone have any channels they recommend to explain differential calculus

[fluid sorrel]

Yeah

But every differentiable function is continuous function

I had to add on that

[wispy widget]

No , are you dumb? It's not true

[fluid sorrel]

The tangent from LHS= tangent from rhs

[wispy widget]

What about y=|x| at x=0

[fluid sorrel]

Sorry it's otherway round

Typp

Typp

Mb

[fluid sorrel]

Its not

[odd ocean]

lmfao

its not complex

it generalizes beautifully

In multivariable calculus the derivative at a is the unique linear map Df(a) such that
f(a+h) = f(a) + Df(a)(h) + o(|h|).
this is exactly the same definition just higher-dimensional the difference quotient definition doesn’t generalize as cleanly

[wispy widget]

Yup but when people learn calculus ,they first begin with 1 variable not multivarible , and as the guy is asking for derivative definition it suggest that he must be a high schooler , so basic single variable definition of derivative is enough to make him understand

[odd ocean]

even in standard hs sense ur definition was wrong

we don't divide actual infinitesimals Instead, we use a limit process

[fluid sorrel]

Ur definition says divide by dx which is wrong... It's not divide it's limit and it shows rate of change

[median spear]

Every function has to be continuous to be differential

[wispy widget]

Yup but a function which is continuos need not be differential

[median spear]

At x=0, LHD is not equal to RHD, (breaking point formed)

So not differentiable

[median spear]

Correct

[wispy widget]

Do you even understand what I told?

[median spear]

i guess i do

[wispy widget]

Read my message again

[median spear]

u said the absolute function is differentiable at zero

[median spear]

..

No offense

[fluid sorrel]

Yooo

Girl

I edited the msg

Before u put that dumb thing

I had put up every continuous is diff which was supposed to be other way around

Chilll 🗿

[wispy widget]

I know , but this loki is saying I am wrong

[median spear]

how is absolute function differentiable at x=0

[wispy widget]

I am telling its not , read my reply again, he was having a misconception that every continuos function is differentiable , that's why I asked him

[median spear]

Fine.

Mb i guess

[fluid sorrel]

😂

Confusion

I get it

[odd ocean]

no need to be rude to people

saying that to someone who called someone dumb