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

Apply Infinity Property:

c - \infty = - \infty

= - \infty

x \to \frac{π}{2} lim (\frac{2 x}{π})

x \to n lim (x)

x \to 0 lim (- 2 sin (3 x))

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

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

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