What is the limit as n approaches infinity of n!+n^3 ?

The limit as n approaches infinity of n!+n^3 is infinity

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limit as n approaches infinity of n!+n^3

n \to \infty lim (n! + n^{3})

\infty

Solution steps

n \to \infty lim (n! + n^{3})

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

With the exception of indeterminate form

= n \to \infty lim (n!) + n \to \infty lim (n^{3})

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

n \to \infty lim (n^{3}) = \infty

= \infty + \infty

Apply Infinity Property:

\infty + \infty = \infty

= \infty

What is the limit as n approaches infinity of n!+n^3 ?
The limit as n approaches infinity of n!+n^3 is infinity