What is the limit as x approaches 0+of (1+x)^{4/x} ?

The limit as x approaches 0+of (1+x)^{4/x} is e^4

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limit as x approaches 0+of (1+x)^{4/x}

x \to 0 + lim ((1 + x)^{\frac{4}{x}})

e^{4}

Decimal Notation

54.59815 \dots

Solution steps

x \to 0 + lim ((1 + x)^{\frac{4}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{4}{x} l n (1 + x)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

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\int_{- 1}^{0} \frac{6}{1 + ( 2 x + 1 ) ^{2}} d x

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What is the limit as x approaches 0+of (1+x)^{4/x} ?
The limit as x approaches 0+of (1+x)^{4/x} is e^4