What is the limit as x approaches infinity of (1+2/x)^{x/8} ?

The limit as x approaches infinity of (1+2/x)^{x/8} is \sqrt[4]{e}

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limit as x approaches infinity of (1+2/x)^{x/8}

x \to \infty lim ((1 + \frac{2}{x})^{\frac{x}{8}})

Decimal Notation

1.28402 \dots

Solution steps

x \to \infty lim ((1 + \frac{2}{x})^{\frac{x}{8}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{8} l n (1 + \frac{2}{x})})

Apply the Limit Chain Rule:

x \to - \infty lim (x - x^{3})

x \to 5 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} - 4 x - 5})

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

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

x \to 4 lim (0)

What is the limit as x approaches infinity of (1+2/x)^{x/8} ?
The limit as x approaches infinity of (1+2/x)^{x/8} is \sqrt[4]{e}