What is the limit as x approaches infinity of (1+5/x)^{x/7} ?

The limit as x approaches infinity of (1+5/x)^{x/7} is e^{5/7}

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limit as x approaches infinity of (1+5/x)^{x/7}

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})

e^{\frac{5}{7}}

Decimal

2.04272 \dots

Solution steps

x \to \infty lim ((1 + \frac{5}{x})^{\frac{x}{7}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{7} l n (1 + \frac{5}{x})})

Apply the Limit Chain Rule:

e^{\frac{5}{7}}

= e^{\frac{5}{7}}

What is the limit as x approaches infinity of (1+5/x)^{x/7} ?
The limit as x approaches infinity of (1+5/x)^{x/7} is e^{5/7}