1. ## HELP!

Use 1' Hopital's Rule t find the limit. SHOW WORK Lim cos x-1 /2x(squared) is 0/0 form.

2. Originally Posted by Emmeyh15@hotmail.com
Use 1' Hopital's Rule t find the limit. SHOW WORK Lim cos x-1 /2x(square root 2) is 0/0 form.

Hi there,

Whenever you have a limit of indeterminate form of type 0/0
just differentiate the top and the bottom separately.

$\displaystyle \frac{d}{dx}(Cos(x)-1)= -Sin(x)$

$\displaystyle \frac{d}{dx}(2x\sqrt{2})=\sqrt{2}\frac{d}{dx}(2x)= 2 \sqrt{2}$

Now you take the limit of f'(x)/g'(x)

$\displaystyle \lim_{x \rightarrow 0}\frac{-sin(x)}{2\sqrt{2}}=0$

NOTE: Here we differentiated only once, but sometimes you have to differentiate multiple times in order to get the limit.

3. Originally Posted by fonso_gfx
Hi there,

Whenever you have a limit of indeterminate form of type 0/0
just differentiate the top and the bottom separately.

$\displaystyle \frac{d}{dx}(Cos(x)-1)= -Sin(x)$

$\displaystyle \frac{d}{dx}(2x\sqrt{2})=\sqrt{2}\frac{d}{dx}(2x)= 2 \sqrt{2}$

Now you take the limit of f'(x)/g'(x)

$\displaystyle \lim_{x \rightarrow 0}\frac{-sin(x)}{2\sqrt{2}}=0$

NOTE: Here we differentiated only once, but sometimes you have to differentiate multiple times in order to get the limit.
you can use \sin(x) and \cos(x) for the trig functions to get $\displaystyle \sin(x)$ $\displaystyle \cos(x)$ in LaTeX

CB