What is the limit as x approaches infinity of (1+1/(6x))^{5x} ?

The limit as x approaches infinity of (1+1/(6x))^{5x} is e^{5/6}

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limit as x approaches infinity of (1+1/(6x))^{5x}

x \to \infty lim ((1 + \frac{1}{6 x})^{5 x})

e^{\frac{5}{6}}

Decimal Notation

2.30097 \dots

Solution steps

x \to \infty lim ((1 + \frac{1}{6 x})^{5 x})

Apply exponent rules

= x \to \infty lim (e^{5 x l n (1 + \frac{1}{6 x})})

Apply the Limit Chain Rule:

e^{\frac{5}{6}}

= e^{\frac{5}{6}}

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

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What is the limit as x approaches infinity of (1+1/(6x))^{5x} ?
The limit as x approaches infinity of (1+1/(6x))^{5x} is e^{5/6}