What is the limit as t approaches infinity of (1-e^{-2t})/t ?

The limit as t approaches infinity of (1-e^{-2t})/t is 0

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limit as t approaches infinity of (1-e^{-2t})/t

t \to \infty lim (\frac{1 - e ^{- 2 t}}{t})

0

Solution steps

t \to \infty lim (\frac{1 - e ^{- 2 t}}{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 - e ^{- 2 t} )}{lim _{t \to \infty} ( t )}

t \to \infty lim (1 - e^{- 2 t}) = 1

t \to \infty lim (t) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

\int \frac{1}{x ^{2} - 2 x + 5} d x

\frac{d}{d x} (arctan (e^{- x}))

e^{3 x}

n \to \infty lim (\frac{n ^{2}}{2 1 ^{n}})

5 t^{2} - 2 e^{t}

What is the limit as t approaches infinity of (1-e^{-2t})/t ?
The limit as t approaches infinity of (1-e^{-2t})/t is 0