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

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

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

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

\infty

Solution steps

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

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

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

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

= 2 \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

= 2 \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

= 2 \cdot 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

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

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

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

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

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