What is the limit as x approaches-3+of (x^3+9)/(x+3) ?

The limit as x approaches-3+of (x^3+9)/(x+3) is -infinity

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limit as x approaches-3+of (x^3+9)/(x+3)

x \to - 3 + lim (\frac{x ^{3} + 9}{x + 3})

- \infty

Solution steps

x \to - 3 + lim (\frac{x ^{3} + 9}{x + 3})

\frac{x ^{3} + 9}{x + 3} = (x^{3} + 9) \frac{1}{x + 3}

= x \to - 3 + lim ((x^{3} + 9) \frac{1}{x + 3})

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 - 3 + lim (x^{3} + 9) \cdot x \to - 3 + lim (\frac{1}{x + 3})

x \to - 3 + lim (x^{3} + 9) = - 18

x \to - 3 + lim (\frac{1}{x + 3}) = \infty

= (- 18) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches-3+of (x^3+9)/(x+3) ?
The limit as x approaches-3+of (x^3+9)/(x+3) is -infinity