What is the limit as t approaches 0 of (e^{5t}-1)/t ?

The limit as t approaches 0 of (e^{5t}-1)/t is 5

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limit as t approaches 0 of (e^{5t}-1)/t

t \to 0 lim (\frac{e ^{5 t} - 1}{t})

5

Solution steps

t \to 0 lim (\frac{e ^{5 t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{5 e ^{5 t}}{1})

= t \to 0 lim (\frac{5 e ^{5 t}}{1})

Plug in the value

t = 0

= \frac{5 e ^{5 \cdot 0}}{1}

Simplify

= 5

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What is the limit as t approaches 0 of (e^{5t}-1)/t ?
The limit as t approaches 0 of (e^{5t}-1)/t is 5