Question

Evaluate:

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

Answer 1

Now,

$\underset{x\to \frac{\pi }{2}}{lim}\frac{2\pi -x}{\cos x}$ $\left(\frac{0}{0}\right)$ form

Now applying the L'Hospital's rule we get,

$=\underset{x\to \frac{\pi }{2}}{lim}\frac{-1}{-\sin x}$

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

$=1$.