What is the limit as x approaches infinity of 6(1+1/x)^{x^2} ?

The limit as x approaches infinity of 6(1+1/x)^{x^2} is infinity

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limit as x approaches infinity of 6(1+1/x)^{x^2}

x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

\infty

Solution steps

x \to \infty lim (6 (1 + \frac{1}{x})^{x^{2}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 6 \cdot x \to \infty lim ((1 + \frac{1}{x})^{x^{2}})

Apply exponent rules

= 6 \cdot x \to \infty lim (e^{x^{2} l n (1 + \frac{1}{x})})

Apply the Limit Chain Rule:

\infty

= 6 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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What is the limit as x approaches infinity of 6(1+1/x)^{x^2} ?
The limit as x approaches infinity of 6(1+1/x)^{x^2} is infinity