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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

x^{2} + \frac{3}{x}

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

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

x \to 0 - lim (\frac{3}{x}) = - \infty

= 0 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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