lim-x-e-x-e-x-e-x-e-x-

Question Number 116252 by bemath last updated on 02/Oct/20

\lim_{x \to - \infty} \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} = ?

Answered by MJS_new last updated on 02/Oct/20

\frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} = \frac{1}{\tanh x} \Rightarrow limit = - 1

or

\frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} = \frac{e^{2 x} + 1}{e^{2 x} - 1} \Rightarrow limit = - 1

Commented by MJS_new last updated on 02/Oct/20

sorry took \infty instead of - \infty

Commented by bemath last updated on 02/Oct/20

thank you sir

Answered by Dwaipayan Shikari last updated on 02/Oct/20

\lim_{x \to - \infty} \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} = \lim_{x \to \infty} \frac{e^{- x} + e^{x}}{e^{- x} - e^{x}} = - 1 ({\underset{x \to \infty}{\lim e}}^{- x} = 0)