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

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

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limit as x approaches infinity of ln(x)x

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

\infty

Solution steps

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to 2 lim (m x)

x \to 0 - lim (x^{x})

x \to 1 lim (\frac{sin ( 2 x )}{x})

x \to \infty lim (- \frac{1}{x} - 1)

x \to 0 + lim ((x^{2})^{x})

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