Question

The $\underset{x\to \frac{\pi }{2}}{lim}\{2x\tan x-\frac{\pi }{\cos x}\}$ is:

• A. $-1$
• B. $-3$
• C. $-2$
• D. $0$

Answer 1

The correct option is C $-2$

$\underset{x\to \frac{\pi }{2}}{lim}\left\{\frac{2x\sin x-\pi }{\cos x}\right\}$
Using L'Hospitals' rule,
$\underset{x\to \frac{\pi }{2}}{lim}\left\{\frac{2\sin x+2x\cos x}{-\sin x}\right\}$
$=-2$