What is the limit as x approaches-2-of (x^3)/(x^2-4) ?

The limit as x approaches-2-of (x^3)/(x^2-4) is -infinity

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limit as x approaches-2-of (x^3)/(x^2-4)

x \to - 2 - lim (\frac{x ^{3}}{x ^{2} - 4})

- \infty

Solution steps

x \to - 2 - lim (\frac{x ^{3}}{x ^{2} - 4})

\frac{x ^{3}}{x ^{2} - 4} = x^{3} \frac{1}{x ^{2} - 4}

= x \to - 2 - lim (x^{3} \frac{1}{x ^{2} - 4})

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 - 2 - lim (x^{3}) \cdot x \to - 2 - lim (\frac{1}{x ^{2} - 4})

x \to - 2 - lim (x^{3}) = - 8

x \to - 2 - lim (\frac{1}{x ^{2} - 4}) = \infty

= (- 8) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to - 1 lim ((2 x + 2) (x + 2))

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

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})

What is the limit as x approaches-2-of (x^3)/(x^2-4) ?
The limit as x approaches-2-of (x^3)/(x^2-4) is -infinity