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

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

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limit as x approaches infinity of xln(x)

x \to \infty lim (x ln (x))

\infty

Solution steps

x \to \infty lim (x ln (x))

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

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

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