What is the limit as t approaches 0 of (e^{4t}-1)/t ?

The limit as t approaches 0 of (e^{4t}-1)/t is 4

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limit as t approaches 0 of (e^{4t}-1)/t

t \to 0 lim (\frac{e ^{4 t} - 1}{t})

4

Solution steps

t \to 0 lim (\frac{e ^{4 t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{4 e ^{4 t}}{1})

= t \to 0 lim (\frac{4 e ^{4 t}}{1})

Plug in the value

t = 0

= \frac{4 e ^{4 \cdot 0}}{1}

Simplify

= 4

5 x^{9} - 2 x^{6}

\frac{6}{s ^{5}}

\frac{d y}{d t} - \frac{8}{t} \cdot y = t^{5}

\frac{d}{d x} ((\frac{x ^{2}}{x ^{2} + 2})^{2})

cos (3 t + 5) e^{2 t}

What is the limit as t approaches 0 of (e^{4t}-1)/t ?
The limit as t approaches 0 of (e^{4t}-1)/t is 4