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

The limit as t approaches infinity of e^{-t} is 0

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limit as t approaches infinity of e^{-t}

t \to \infty lim (e^{- t})

0

Solution steps

t \to \infty lim (e^{- t})

Simplify

e^{- t} : \frac{1}{e ^{t}}

= t \to \infty lim (\frac{1}{e ^{t}})

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 _{t \to \infty} ( 1 )}{lim _{t \to \infty} ( e ^{t} )}

t \to \infty lim (1) = 1

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

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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What is the limit as t approaches infinity of e^{-t} ?
The limit as t approaches infinity of e^{-t} is 0