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

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

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limit as x approaches infinity of ax^2

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

\infty

Solution steps

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

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

= a \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

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

Apply the common limit:

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

= a \infty^{2}

Simplify

a \infty^{2} : \infty

= \infty

\int \frac{3 x}{e ^{x}} d x

\frac{d}{d x} (x^{2} sin (\frac{1}{a x}))

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

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

x \to 4 lim (x^{2} + 9)

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