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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int \frac{1}{x ^{2} + 36} d x

x \to - \infty lim (\frac{x ^{2} + 2}{x ^{3} + x ^{2} - 1})

x \to 0 lim (7 x^{3} + \frac{1}{4} x^{2})

\frac{\partial}{\partial y} (x \cdot ln (x + 2 y) + \frac{x}{y})

f (x) = \frac{1}{x + 2}

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