What is the limit as x approaches 0-of (x^3-2)/x ?

The limit as x approaches 0-of (x^3-2)/x is infinity

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limit as x approaches 0-of (x^3-2)/x

x \to 0 - lim (\frac{x ^{3} - 2}{x})

\infty

Solution steps

x \to 0 - lim (\frac{x ^{3} - 2}{x})

Expand

\frac{x ^{3} - 2}{x} : x^{2} - \frac{2}{x}

= x \to 0 - lim (x^{2} - \frac{2}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 - lim (x^{2}) - x \to 0 - lim (\frac{2}{x})

x \to 0 - lim (x^{2}) = 0

x \to 0 - lim (\frac{2}{x}) = - \infty

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

What is the limit as x approaches 0-of (x^3-2)/x ?
The limit as x approaches 0-of (x^3-2)/x is infinity