What is the limit as x approaches-3+of (x^2+9)/(x+3) ?

The limit as x approaches-3+of (x^2+9)/(x+3) is infinity

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limit as x approaches-3+of (x^2+9)/(x+3)

x \to - 3 + lim (\frac{x ^{2} + 9}{x + 3})

\infty

Solution steps

x \to - 3 + lim (\frac{x ^{2} + 9}{x + 3})

\frac{x ^{2} + 9}{x + 3} = (x^{2} + 9) \frac{1}{x + 3}

= x \to - 3 + lim ((x^{2} + 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^{2} + 9) \cdot x \to - 3 + lim (\frac{1}{x + 3})

x \to - 3 + lim (x^{2} + 9) = 18

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

= 18 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 2 lim (5 - 2 x)

x \to \infty lim (\frac{sin ( 5 x )}{5 x})

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

x \to 0 lim (\frac{1}{4})

x \to 0 lim (\frac{1}{- x})

What is the limit as x approaches-3+of (x^2+9)/(x+3) ?
The limit as x approaches-3+of (x^2+9)/(x+3) is infinity