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

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

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

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

- 1

Solution steps

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

Simplify

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

Apply L'Hopital's Rule

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

Plug in the value

t = 0

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

Simplify

= - 1

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