What is the limit as x approaches 0+of (1+8/x)^{6x} ?

The limit as x approaches 0+of (1+8/x)^{6x} is 1

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limit as x approaches 0+of (1+8/x)^{6x}

x \to 0 + lim ((1 + \frac{8}{x})^{6 x})

1

Solution steps

x \to 0 + lim ((1 + \frac{8}{x})^{6 x})

Apply exponent rules

= x \to 0 + lim (e^{6 x l n (1 + \frac{8}{x})})

Apply the Limit Chain Rule:

1

= 1

x \to \infty lim (1 \frac{1}{x})

x \to \infty lim (- 6)

x \to - 7 lim (\frac{x - 6}{x + 7})

x \to 1 lim (x^{2} - 4 x + 1)

x \to 2 - lim (\frac{x ^{3} - 4}{x - 2})

What is the limit as x approaches 0+of (1+8/x)^{6x} ?
The limit as x approaches 0+of (1+8/x)^{6x} is 1