lim-x-0-1-tanx-cotx-

Question Number 28095 by tawa tawa last updated on 20/Jan/18

\lim_{x \to 0^{-}} {(1 + tanx)}^{- cotx}

Commented by abdo imad last updated on 20/Jan/18

= {l i m}_{x \to 0^{-}} e^{- c o t a n x l n (1 + t a n x)} b u t

l n (1 + t a n x)_{x \in V (0)} \sim t a n x \Rightarrow - c o t a n x l n (1 + t a n x)

\sim - \frac{t a n x}{t a n x} = - 1 \Rightarrow {l i m}_{x \to 0^{-}} {(1 + t a n x)}^{- c o t a n x} = \frac{1}{e} .

Commented by tawa tawa last updated on 21/Jan/18

God bless you sir