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

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

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

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

\infty

Solution steps

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

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

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

= \frac{\infty}{1}

Apply Infinity Property:

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

= \infty

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