What is the limit as x approaches infinity of xn(x) ?

The limit as x approaches infinity of xn(x) is infinity

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limit as x approaches infinity of xn(x)

x \to \infty lim (x n (x))

\infty

Solution steps

x \to \infty lim (x n x)

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

= n \cdot x \to \infty lim (xx)

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

With the exception of indeterminate form

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

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

= n \cdot \infty \cdot \infty

Simplify

n \cdot \infty \cdot \infty : \infty

= \infty

What is the limit as x approaches infinity of xn(x) ?
The limit as x approaches infinity of xn(x) is infinity