What is the limit as x approaches 3-of (4x)/(9-x^2) ?

The limit as x approaches 3-of (4x)/(9-x^2) is infinity

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limit as x approaches 3-of (4x)/(9-x^2)

x \to 3 - lim (\frac{4 x}{9 - x ^{2}})

\infty

Solution steps

x \to 3 - lim (\frac{4 x}{9 - x ^{2}})

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

= 4 \cdot x \to 3 - lim (\frac{x}{9 - x ^{2}})

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

= 4 \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

= 4 \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

= 4 \cdot 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 6 + lim (5 x - 12)

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

x \to 3 lim (2 x^{2} + 5 x + 3)

x \to 3 - lim (x - 5)

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

What is the limit as x approaches 3-of (4x)/(9-x^2) ?
The limit as x approaches 3-of (4x)/(9-x^2) is infinity