Question

$\displaystyle\lim_{x\to \frac{\pi}{2}} \frac{\cos \, x}{ x - \frac{\pi}{2}}$ equals:

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

Answer 1

Answer: (B)

-1

Answer 2

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