Two Trig Limits YOU NEED for AP Calc Exam

These are two fundamental trig limits you're expected to know on the AP Calculus AB and AP Calculus BC exams. You can use these limits to solve a variety of other limit problems. The first is the limit of sinx/x as x approaches 0, which equals 1. The second is the limit of (1-cosx)/x as x approaches 0, which is 0. We solve an example trig limit problem using each fact. #apcalculus #shorts

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[Dan_Animation]

Thx so much, I'm in 4th grade and it's very hard to do these concepts on my own. I can now ace my exam thanks to you

[mikes]

Well, that brings on my Calculus PTSD.

[shivanshnigam]

If you put an x² at the bottom instead of an x in the cosine limit it becomes 1/2

[nailedthepotato]

A must know rule when solving limits: L'Hopital
L'Hopital rule states:
If you have function f(x) and g(x) that approaches an indeterminate form as x->c then:
Lim f(x)/g(x) = lim f`(x)/g`(x)
x->c x->c

Let's take the first example:
Lim sin(x)/x
x->0
Sin(0)/0 = 0/0
Let's define: f(x)=sin(x), g(x)=x
f`(x)=cos(x), g`(x)=1
lim cos(x) = cos(0) = 1
x->0

[PadPaper]

Baby Step: Memorize that six(x)/x is undefined at zero. However, it’s right and left side limit equal 1.

Child Steps: Know how to manipulate and substitute values of limits.

Big Kids Step: Now prove that the limit of x -> 0 of sin(x)/x equals 1. Hint, start with “for all epsilon>0, there exists a positive integer N such that…”. Some Elementary Analysis may be needed.

[danielkelsosmith]

Weird; I literally just got to this section last week and I get this video recommended

[Akshuu-ugki]

Can you tell me if it's hard or not

[domdom-hhtx]

literally where the fuck were u? i had a long exam yesterday in calc T_T anyways glad that this vid will help everyone <333

[jackbrax]

Or you could simply use L’hoptials rule

[StarRailEnjoyerSinceRelease]

My brain ain't braining.

I don't have X so why should I find Y?😢

[thataialaperrera]

I just want to be taught how trigonometry in calculus is used in the real world, cause I know it is used in the real world if they teach me it, just teach me HOW AND WHERE it is used 😭

[Rando]

Proof: using geometry. a circle setup should work

[ExcommAvo]

Why is there a cosx in the denominator being multiplied by an x in the second part after 1 was converted to cosx/cosx?

[oppositexo]

I’m confused you can change 1 to cosx/cosx?

[hlopplopp]

You can literally just ise l'hôpital's rule for the last one

[TheBluePhoenix]

That's the most basic limit though😭

[cptn_nm]

Or just know sin(x) ~ x when x is near 0

[preethamsartgaming]

Bro no need of that much elongation we can just remember it as sinax/x=a

[davidmurphy]

I don't think the meds are working.

[ossigaming]

Bro, first part is wrong. Sin(x) is a function. For sin(4x), you can't just do 4/4 * sin(4x) to get 4*sin(x). You can compare that with Desmos. What actually changes is the rate of change of the function at x=0. This gets combined with the fact, that the Taylor Series of sin(x) begins with x. So Sin(4x) is = 4x, as you approch zero. But no more. Only because of this, does your calculation at the beginning work.