What is the limit as x approaches infinity of (1+8/x)^{x/9} ?

The limit as x approaches infinity of (1+8/x)^{x/9} is e^{8/9}

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limit as x approaches infinity of (1+8/x)^{x/9}

x \to \infty lim ((1 + \frac{8}{x})^{\frac{x}{9}})

e^{\frac{8}{9}}

Decimal

2.43242 \dots

Solution steps

x \to \infty lim ((1 + \frac{8}{x})^{\frac{x}{9}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{9} l n (1 + \frac{8}{x})})

Apply the Limit Chain Rule:

e^{\frac{8}{9}}

= e^{\frac{8}{9}}

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What is the limit as x approaches infinity of (1+8/x)^{x/9} ?
The limit as x approaches infinity of (1+8/x)^{x/9} is e^{8/9}