lim (1-cosx)^2 / x
x- 0

Question

lim (1-cosx)^2 / x 
x-> 0

parthkohli · Answer

$${d \over dx}\left({(1 - \cos x)^2 \over x} \right) = \quad? $$

parthkohli · Answer

Keep differentiating. :)

anonymous · Answer

umm could you please explain where you got the d/dx ?

parthkohli · Answer

Sorry... wait

parthkohli · Answer

$$\left({{d\over dx}(1 - \cos x)^2 \over {d \over dx}(x)}\right) $$

anonymous · Answer

@ParthKohli Please try to not use l'Hospital's for simple limits. Most people have just started calculus, currently. And, in addition, you need to differentiate both the numerator and denominator.

parthkohli · Answer

Okay, then graphing?

parthkohli · Answer

@LolWolf Yes... fixed that just before your reply :)

anonymous · Answer

im also fine with the law of limits but im not sure about the other one

anonymous · Answer

I'd recommend using the rules given (that can be proven geometrically). i.e.
$$
\lim_{x\to0}\frac{1-\cos(x)}{x}=0
$$And
$$
\lim_{x\to0}\frac{\sin(x)}{x}=1
$$

parthkohli · Answer

Try graphing the function using technology, then see how the function goes towards 0.

hartnn · Answer

u can do it like this:
|dw:1346993722105:dw|
use the formula sin x/x for 1st fraction
and directly substitute x=0 in 2nd fraction.
did u get it?