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

The limit as x approaches-infinity of e^x+e^{-x} is infinity

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limit as x approaches-infinity of e^x+e^{-x}

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

\infty

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to - \infty lim (e^{x}) = 0

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

= 0 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

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