What is the limit as x approaches infinity of (1+1/(7x))^{9x} ?

The limit as x approaches infinity of (1+1/(7x))^{9x} is e^{9/7}

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limit as x approaches infinity of (1+1/(7x))^{9x}

x \to \infty lim ((1 + \frac{1}{7 x})^{9 x})

e^{\frac{9}{7}}

Decimal

3.61725 \dots

Solution steps

x \to \infty lim ((1 + \frac{1}{7 x})^{9 x})

Apply exponent rules

= x \to \infty lim (e^{9 x l n (1 + \frac{1}{7 x})})

Apply the Limit Chain Rule:

e^{\frac{9}{7}}

= e^{\frac{9}{7}}

What is the limit as x approaches infinity of (1+1/(7x))^{9x} ?
The limit as x approaches infinity of (1+1/(7x))^{9x} is e^{9/7}