What is the limit as x approaches 0 of (1+5x)^{6/x} ?

The limit as x approaches 0 of (1+5x)^{6/x} is e^{30}

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limit as x approaches 0 of (1+5x)^{6/x}

x \to 0 lim ((1 + 5 x)^{\frac{6}{x}})

e^{30}

Decimal

1.06865 E 13

Solution steps

x \to 0 lim ((1 + 5 x)^{\frac{6}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{6}{x} l n (1 + 5 x)})

Apply the Limit Chain Rule:

e^{30}

= e^{30}

What is the limit as x approaches 0 of (1+5x)^{6/x} ?
The limit as x approaches 0 of (1+5x)^{6/x} is e^{30}