# Math Help - Need Calculus I Help!!!!

1. ## Need Calculus I Help!!!!

I need help asap with a cal I question dealing with limits.
The question:

lim (1-cos sqrt(x)) / x
x->0

Please explain how its worked out....thanks in advance...

2. Originally Posted by shopgirl
I need help asap with a cal I question dealing with limits.
The question:

lim (1-cos sqrt(x)) / x
x->0

Please explain how its worked out....thanks in advance...
this limit goes to 0/0, you can apply L'Hopital's rule, which basically says: $\lim \frac {f(x)}{g(x)} = \lim \frac {f'(x)}{g'(x)}$

3. I hate L'Hôpital (unless the limit be very messy)

Rewrite the limit as follows

$\lim_{x\to0}\frac{1-\cos\sqrt x}x=\lim_{x\to0}\frac{\sin^2\sqrt x}{x(1+\cos\sqrt x)}=\lim_{x\to0}\left[\left(\frac{\sin\sqrt x}{\sqrt x}\right)^2\cdot\frac1{1+\cos\sqrt x}\right]$

Does that make sense?