What is the limit as x approaches infinity of (1+3/x)^{x/4} ?

The limit as x approaches infinity of (1+3/x)^{x/4} is e^{3/4}

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limit as x approaches infinity of (1+3/x)^{x/4}

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

e^{\frac{3}{4}}

Decimal

2.11700 \dots

Solution steps

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{4} l n (1 + \frac{3}{x})})

Apply the Limit Chain Rule:

e^{\frac{3}{4}}

= e^{\frac{3}{4}}

What is the limit as x approaches infinity of (1+3/x)^{x/4} ?
The limit as x approaches infinity of (1+3/x)^{x/4} is e^{3/4}