What is the limit as x approaches 0+of (1+5x)^{3/x} ?

The limit as x approaches 0+of (1+5x)^{3/x} is e^{15}

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limit as x approaches 0+of (1+5x)^{3/x}

x \to 0 + lim ((1 + 5 x)^{\frac{3}{x}})

e^{15}

Decimal

3269017.37247 \dots

Solution steps

x \to 0 + lim ((1 + 5 x)^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + 5 x)})

Apply the Limit Chain Rule:

e^{15}

= e^{15}

What is the limit as x approaches 0+of (1+5x)^{3/x} ?
The limit as x approaches 0+of (1+5x)^{3/x} is e^{15}