Question

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

Answer 1

${lim}_{x\to 1}\frac{\cos \frac{\pi }{2}x}{1-x}=\frac{0}{0}$

Applying L-Hospital's rule

$={lim}_{x\to 1}\frac{+\frac{\pi }{2}\sin \frac{\pi }{2}x}{+1}=\frac{\pi }{2}\sin \frac{\pi }{2}=\frac{\pi }{2}$