What is the limit as x approaches 0+of (1+6x)^{3/x} ?

The limit as x approaches 0+of (1+6x)^{3/x} is e^{18}

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limit as x approaches 0+of (1+6x)^{3/x}

x \to 0 + lim ((1 + 6 x)^{\frac{3}{x}})

e^{18}

Decimal Notation

65659969.13733 \dots

Solution steps

x \to 0 + lim ((1 + 6 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + 6 x)})

Apply the Limit Chain Rule:

e^{18}

= e^{18}

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What is the limit as x approaches 0+of (1+6x)^{3/x} ?
The limit as x approaches 0+of (1+6x)^{3/x} is e^{18}