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

The limit as x approaches 0 of (x+e^x)^{1/x} is e^2

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limit as x approaches 0 of (x+e^x)^{1/x}

x \to 0 lim ((x + e^{x})^{\frac{1}{x}})

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

x \to 0 lim ((x + e^{x})^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (x + e^{x})})

Apply the Limit Chain Rule:

e^{2}

= e^{2}

\frac{d}{d x} (ln (x^{l n (x)}))

x \to 0 lim (1 + x^{2})

f (x) = x^{7} cos (x)

y^{^{'}} = x (e + y)

x \to \infty lim (3 x^{2} - 8)

What is the limit as x approaches 0 of (x+e^x)^{1/x} ?
The limit as x approaches 0 of (x+e^x)^{1/x} is e^2