What is the limit as x approaches 0 of (1+8x)^{5/x} ?

The limit as x approaches 0 of (1+8x)^{5/x} is e^{40}

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limit as x approaches 0 of (1+8x)^{5/x}

x \to 0 lim ((1 + 8 x)^{\frac{5}{x}})

e^{40}

Decimal

2.35385 E 17

Solution steps

x \to 0 lim ((1 + 8 x)^{\frac{5}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{5}{x} l n (1 + 8 x)})

Apply the Limit Chain Rule:

e^{40}

= e^{40}

What is the limit as x approaches 0 of (1+8x)^{5/x} ?
The limit as x approaches 0 of (1+8x)^{5/x} is e^{40}