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

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

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

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

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{4}

= e^{4}

\frac{d}{d t} (1 - t^{2})

\frac{\partial}{\partial x} (\frac{4}{x y})

\frac{d y}{d t} = e^{2 (t)} - 3 y, y (0) = 1

\int_{- 1}^{0} 3 u + 4 d u

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