Limits

[glad palm]

Its coming indeterment

[static heath]

do you need any help

@glad palm

it's good to see it this way

a limit will have two sides that are equal to each other if the limit exists

you go from the left or from the right

those are called left and right limits

often denoted with + or - above the value

i. e.

$\lim_{x\to 0^+}f(x)$

[lyric basalt]

chudcel

[static heath]

we also say a limit exists if

$\lim_{x\to c^+}f(x)=\lim_{x\to c^-}f(x)$

[lyric basalt]

chudcel

[static heath]

and the value of the limit is also those

or actually nah i don't think all of this yap was necessary

just apply l'hopital's rule

i thought there was something like 1/x inside the argument

[glad palm]

What's that?

[static heath]

it's a very powerful tool for these problems

here's what it says

if f, g are continuous and differentiable and $\lim_{x\to c}f(x)=\lim_{x\to c}g(x)=0$, then $\frac{\lim_{x\to c}f(x)}{\lim_{x\to c}g(x)}=\frac{\lim_{x\to c}f'(x)}{\lim_{x\to c}g'(x)}$, where $\lim_{x\to c}g'(x)\neq0$

[glad palm]

I converted it in sin form

I was hoping i could use sinx/x

[lyric basalt]

chudcel

[static heath]

the last part is more important because anyways you are dealing with the quotient of two continuous, differentiable functions

[glad palm]

So i just need to differentiate the whole thing?

Show ur work

[static heath]

yeah the numerator and denominator

if you get 0/0

in this case i see it happening a lot

[glad palm]

Damn this rule is crazy. You can just apply it anywhere or is there any exceptions

[static heath]

yeah it works only for 0/0

it even works for oo/oo

[haughty temple]

[glad palm]

But teachers won't give marks if I do this way

[static heath]

if that's the case i'd use it to find the limit so i can guide myself to the answer

[glad palm]

Can I keep differentiating unless I get the answer that doesn't come 0/0

[static heath]

yes

[glad palm]

Daymen

Yeah but we cant use this rule in exam

No cant.

Teachers won't give marks

[static heath]

men can't you use sinx/x limit here

you multiply 1/x on both

5x6 on both

then you get answer

[glad palm]

What to expand here vro?

[static heath]

this works too

[static heath]

@glad palm do they allow you to use this limit

like

$\lim_{x\to 0}\frac{\sin(x)}{x}=1$

[glad palm]

Yes, sinx/x = 1 and tanx/x=1, in school you can cut perform anything you want but ultimately you have to bring answer using this formula

[lyric basalt]

chudcel

[static heath]

you can do this

[glad palm]

What's cos expansion?

[lyric basalt]

Waltuh

[glad palm]

Bro dont know this formula

I know 1-sin^2x/2 = cos x

Is this from binomial expansion?

I did that chapter

[glad palm]

Bro

Yeah didnt do this chapter, maybe next year

In next class

Cross multiplied

[static heath]

that's 5/6

waht happened

[glad palm]

Why

It can be

Limits split right

Wha

See i divided 5x/2 and multiplied it in other side same with 3x, ultimately if you calculate the result will be same since both 5x/2 and 3x will be elimniated

I basically arranged it in a way so that I can perform this formula sinx/x

[ocean rain]

wait guys
lt sin(x)/x = 1
x->0

sooo multiply and divide perhaps?

(i might be wrong tho so please feel free to correct me if you see a problem)

[static heath]

it's squared so the limit identity won't really work here

[ocean rain]

oh.

[static heath]

i genuinely want to use squeeze theorem on this but it doesn't seem very obvious on what bounds i can use

[ocean rain]

hm

did you try google for this?

i mean...

[static heath]

no i don't use google to solve problems

i have to do it on my own

[ocean rain]

i see

also why will the limit not work when its squared?

coz if im not wrong
lt x->0 sin^2 (x) / x^2 = 1
still holds right?

we can move the limit inside right
[lt x->0 sin(x)/x]^2 ?

[glad palm]

In above it should be 25x^2/4

Why did u only multiply by 25x^2?

I should be 25x^2/4

[glad palm]

Limits will work even squared

Thats not the problem

[ocean rain]

yesyes my mistake sorry

corrected it tho

[ocean rain]

sooo-

what is then?

ah...my bad

[glad palm]

Its correct

Your answer after correction is right

[ocean rain]

yay

[glad palm]

25/36 should be coming

[ocean rain]

yea i got that after i corrected the "divide by 4"

idk how i made that mistake my bad