What is the limit as t approaches 0 of (2e^t-2)/t ?

The limit as t approaches 0 of (2e^t-2)/t is 2

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limit as t approaches 0 of (2e^t-2)/t

t \to 0 lim (\frac{2 e ^{t} - 2}{t})

2

Solution steps

t \to 0 lim (\frac{2 e ^{t} - 2}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{2 e ^{t}}{1})

= t \to 0 lim (\frac{2 e ^{t}}{1})

Plug in the value

t = 0

= \frac{2 e ^{0}}{1}

Simplify

= 2

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