What is the limit as n approaches infinity of nln(n) ?

The limit as n approaches infinity of nln(n) is infinity

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limit as n approaches infinity of nln(n)

n \to \infty lim (n ln (n))

\infty

Solution steps

n \to \infty lim (n ln (n))

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

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

What is the limit as n approaches infinity of nln(n) ?
The limit as n approaches infinity of nln(n) is infinity