lim-x-pi-x-pi-sinx-

Question Number 184891 by mathlove last updated on 13/Jan/23

\lim_{x \to π} \frac{x - π}{s i n x} = ?

Answered by Mathspace last updated on 13/Jan/23

c h a n g . x - π = t g i v e

{l i m}_{x \to π} \frac{x - π}{s i n x} = {l i m}_{t \to 0} \frac{t}{s i n (π + t)}

= - {l i m}_{t \to 0} \frac{t}{s i n t} = - 1

Answered by alephzero last updated on 13/Jan/23

\lim_{x \to π} \frac{x - π}{\sin x} = \lim_{x \to π} \frac{1}{\cos x} = \frac{1}{- 1} = - 1

Answered by TUN last updated on 14/Jan/23

= \lim_{x \to π} \frac{- (π - x)}{s i n (π - x)}

= - \lim_{x \to π} \frac{π - x}{s i n (π - x)}

= - 1

Facebook Tweet Pin