What is the limit as t approaches 0 of (e^{3t}-1)/t ?

The limit as t approaches 0 of (e^{3t}-1)/t is 3

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limit as t approaches 0 of (e^{3t}-1)/t

t \to 0 lim (\frac{e ^{3 t} - 1}{t})

3

Solution steps

t \to 0 lim (\frac{e ^{3 t} - 1}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{3 e ^{3 t}}{1})

= t \to 0 lim (\frac{3 e ^{3 t}}{1})

Plug in the value

t = 0

= \frac{3 e ^{3 \cdot 0}}{1}

Simplify

= 3

x \to \infty + lim (\frac{1}{x} + 4)

\frac{d}{d x} (\frac{6}{x - 1})

\int_{0}^{1} 3 - x^{2} d x

\frac{d y}{d t} - 26 t^{12} e^{- y} = 0

\frac{2}{( x + 1 ) ^{3}}

What is the limit as t approaches 0 of (e^{3t}-1)/t ?
The limit as t approaches 0 of (e^{3t}-1)/t is 3