Question

Limit as x approaches pi/2 of cos(x)/x-(pi/2)

Answer 1

You have a case of 0/0, so use l'hospital's rule:
\[\lim_{x \rightarrow \frac{\pi}{2}} \frac{\cos(x)}{x-\frac{\pi}{2}}=\lim_{x \rightarrow \frac{\pi}{2}}\frac{\frac{d}{dx}\cos(x)}{\frac{d}{dx}(x-\frac{\pi}{2})}=\lim_{x \rightarrow \frac{\pi}{2}} \frac{-\sin(x)}{1}=-1\]

Answer 2

Thanks. We haven't gotten to l'hopital's rule yet (in my calc class), so we're doing this by algebraic manipulation. I had hit a wall, though, and hoped someone could give me some a suggestion as to how I might proceed assuming derivatives can't be used.

Answer 3

*give me a suggestion