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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

t = 0

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

Simplify

= 1

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