What is the limit as x approaches infinity of x^e ?

The limit as x approaches infinity of x^e is infinity

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limit as x approaches infinity of x^e

x \to \infty lim (x^{e})

\infty

Solution steps

x \to \infty lim (x^{e})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (x \to \infty lim (x))^{e}

Apply the common limit:

x \to \infty lim (x) = \infty

= \infty^{e}

Apply Infinity Property:

\infty^{c} = \infty

= \infty

x \to 0 + lim (4 x ln (x))

x \to - \infty lim (\frac{6}{x})

x \to 0 lim (3 x cot (2 x))

x \to 0 - lim (\frac{2}{x ^{3}})

x \to 0 lim ((1 - x^{2})^{\frac{1}{x}})

What is the limit as x approaches infinity of x^e ?
The limit as x approaches infinity of x^e is infinity