What is the limit as x approaches infinity of (1-e-x)/(1+e^{-x)} ?

The limit as x approaches infinity of (1-e-x)/(1+e^{-x)} is -infinity

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limit as x approaches infinity of (1-e-x)/(1+e^{-x)}

x \to \infty lim (\frac{1 - e - x}{1 + e ^{- x}})

- \infty

Solution steps

x \to \infty lim (\frac{1 - e - x}{1 + e ^{- x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to \infty lim (1 - e - x) = - \infty

x \to \infty lim (1 + e^{- x}) = 1

= \frac{- \infty}{1}

Apply Infinity Property:

\frac{- \infty}{c} = - \infty

= - \infty

\frac{e ^{2 x}}{x + 1}

n = 6 \sum \infty \frac{1}{n ^{3}}

\int \frac{1}{8 x} d x

\frac{d y}{d x} = \frac{x ^{6} - 2 y}{x}

\frac{\partial}{\partial y} (x y^{2} cos (2 + x^{2} y))

What is the limit as x approaches infinity of (1-e-x)/(1+e^{-x)} ?
The limit as x approaches infinity of (1-e-x)/(1+e^{-x)} is -infinity