Question

Evaluate:

$\underset{x\to \frac{\pi }{2}}{lim}\frac{\log (1+a\cos x)}{\cos x}$, $a$ being a finite number.

• A. $a^2$
• B. $2a$
• C. $a$
• D. none of these

Answer 1

The correct option is C $a$

Now,

$\underset{x\to \frac{\pi }{2}}{lim}\frac{\log (1+a\cos x)}{\cos x}$ $\left(\frac{0}{0}\right)$ form

Now applying L'Hospital's rule we get,

$=\underset{x\to \frac{\pi }{2}}{lim}\frac{\frac{-a\sin x}{(1+a\cos x)}}{-\sin x}$

$=\frac{-a}{-1}$

$=a$.