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

The limit as t approaches 0 of (t+e^t)^{2/t} is e^4

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limit as t approaches 0 of (t+e^t)^{2/t}

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

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

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

Apply exponent rules

= t \to 0 lim (e^{\frac{2}{t} l n (t + e^{t})})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

\frac{d x}{3 d t} - 2 e^{- t} = - x

\frac{\partial}{\partial y} (x z)

\frac{\partial}{\partial x} (3 e^{2 x})

\frac{1}{s ^{2} ( s ^{2} + 25 )}

\int a x d x

What is the limit as t approaches 0 of (t+e^t)^{2/t} ?
The limit as t approaches 0 of (t+e^t)^{2/t} is e^4