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

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

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

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

\infty

Solution steps

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

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 (f (x)) \cdot x \to \infty lim (x^{2})

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

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

= f \cdot \infty \cdot \infty

Simplify

f \cdot \infty \cdot \infty : \infty

= \infty

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