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

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

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

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

\infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

\frac{x}{9 - x ^{2}} = x \frac{1}{9 - x ^{2}}

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

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

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

x \to - 3 - lim (x) = - 3

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

= 3 (- 3) (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

x \to 0 + lim ((x^{2} + 1) ln (x))

x \to 6 lim (3 x - 4)

x \to 0 lim ((1)^{\frac{1}{x ^{2}}})

x \to 0 lim (\frac{1}{2 + x})

x \to 0 lim (e^{\frac{1}{x}} x^{2})

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