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

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

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

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

e^{2}

Decimal Notation

7.38905 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{2}

= e^{2}

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

\int \frac{20 x}{1 - x ^{4}} d x

\int \frac{1}{4 + 2 x} d x

y = x^{3} + 7 x - 5, (1, 3)

\int \frac{8 x ^{3}}{( x ^{2} + 2 ) ^{2}} d x

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