What is the limit as x approaches infinity of x^2y^2 ?

The limit as x approaches infinity of x^2y^2 is infinity

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limit as x approaches infinity of x^2y^2

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

\infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= y^{2} \cdot 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

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

Apply the common limit:

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

= y^{2} \infty^{2}

Simplify

y^{2} \infty^{2} : \infty

= \infty

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What is the limit as x approaches infinity of x^2y^2 ?
The limit as x approaches infinity of x^2y^2 is infinity