lim-x-pi-2-sin-x-cos-x-tan-x-

Question Number 70653 by naka3546 last updated on 06/Oct/19

\lim_{x \to \frac{π}{2}} {(\sin x - \cos x)}^{\tan x} = \dots

Commented by kaivan.ahmadi last updated on 06/Oct/19

{l i m}_{x \to \frac{π}{2}} (s i n x - c o s x - 1) t a n x =

{l i m}_{x \to \frac{π}{2}} ({s i n}^{2} x - s i n x - t a n x) = - \infty

\Rightarrow {l i m}_{x \to \frac{π}{2}} {(s i n x - c o s x)}^{t a n x} = e^{- \infty} = 0

Answered by sadimuhmud 136 last updated on 06/Oct/19