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

The limit as x approaches 0+of (e^x+x)^{4/x} is e^8

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

x \to 0 + lim ((e^{x} + x)^{\frac{4}{x}})

e^{8}

Decimal Notation

2980.95798 \dots

Solution steps

x \to 0 + lim ((e^{x} + x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{4}{x} l n (e^{x} + x)})

Apply the Limit Chain Rule:

e^{8}

= e^{8}

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What is the limit as x approaches 0+of (e^x+x)^{4/x} ?
The limit as x approaches 0+of (e^x+x)^{4/x} is e^8