Question

$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\cos x}{x-\frac{\pi }{2}}$ equals:

• A. - 6
• B. -1
• C. $\pi$
• D. $-\pi$

Answer 1

Answer: (B)

Let $f(x)=\underset{x\to \frac{\pi }{2}}{\lim }\frac{\cos x}{x-\frac{\pi }{2}}$
Put $x-\frac{\pi }{2}=h$
When $x\to \pi /2,h\to 0$
$\therefore \underset{h\to 0}{\lim }\frac{\cos \left(\frac{\pi }{2}+h\right)}{h}=-\underset{h\to 0}{\lim }\frac{\sin h}{h}=-1$