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...
I hate L'Hôpital (unless the limit be very messy)
Rewrite the limit as follows
$\displaystyle \lim_{x\to0}\frac{1-\cos\sqrt x}x=\lim_{x\to0}\frac{\sin^2\sqrt x}{x(1+\cos\sqrt x)}=\lim_{x\to0}\left[\left(\frac{\sin\sqrt x}{\sqrt x}\right)^2\cdot\frac1{1+\cos\sqrt x}\right]$
Does that make sense?