Question

Solve $\underset{x\to 1}{lim}\frac{\cos \frac{\pi }{2}x}{1-x}$

Answer 1

The limit is given as,

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

$=\frac{0}{0}$

This gives the indeterminate form, therefore, differentiating the given limit with respect to $x$, (Using L'hospital rule)

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

$=1$