What is the limit as x approaches infinity of 3^xx! ?

The limit as x approaches infinity of 3^xx! is infinity

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limit as x approaches infinity of 3^xx!

x \to \infty lim (3^{x} x!)

\infty

Solution steps

x \to \infty lim (3^{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 (3^{x}) \cdot x \to \infty lim (x!)

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

x \to 1 lim (e^{\frac{1}{x ^{2} - 1}})

x \to - 1 lim (\frac{e ^{x^{2}} - 1}{x})

x \to - 2 lim (x - x^{2})

x \to 0 lim (\frac{x ^{4}}{1 + x ^{5}})

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

What is the limit as x approaches infinity of 3^xx! ?
The limit as x approaches infinity of 3^xx! is infinity