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

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

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

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

e^{8}

Decimal

2980.95798 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{8}

= e^{8}

x \to 7 lim (\frac{4 x}{x - 7})

x \to - 2 + lim (tan (\frac{π x}{4}))

x \to - 1 lim (2 - x^{2})

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

x \to 0 lim (- \frac{1}{2 x ^{2}})

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