Question

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

Answer 1

$\underset{x\to \frac{\pi }{2}}{lim}\frac{2x-\pi }{\cos x}=\frac{0}{0}$ form

Using 'L' Hospital's rule, we get

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

$=\frac{2}{\sin \frac{\pi }{2}}$

$=\frac{2}{(-1)}$

$=-2$

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