Question

Find the limit :-
$\underset{x\to 1}{lim}\frac{1-\frac{1}{x}}{\sin \pi (x-1)}$

Answer 1

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

Apply $L$ Hospital rule

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

$=\frac{1}{\pi \times 1}$

$=\frac{1}{\pi }$