What is the limit as x approaches infinity of (x!)^2 ?

The limit as x approaches infinity of (x!)^2 is infinity

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limit as x approaches infinity of (x!)^2

x \to \infty lim ((x!)^{2})

\infty

Solution steps

x \to \infty lim (x!^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (x \to \infty lim (x!))^{2}

Apply the common limit:

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

= \infty^{2}

Apply Infinity Property:

\infty^{c} = \infty

= \infty

x^{2} - 12, 4 x

y = (x + 3)^{3}, at x = - \frac{1}{75}

\frac{d}{d x} (\frac{2}{( 2 - x ) ^{2}})

\frac{d}{d x} (\frac{2}{3} (x^{2} - 1)^{\frac{3}{2}})

\frac{d}{d x} (arctan (5 x^{2} - 1))

What is the limit as x approaches infinity of (x!)^2 ?
The limit as x approaches infinity of (x!)^2 is infinity