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

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

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

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

\infty

Solution steps

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

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

= 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

= 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 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

x \to π lim (2^{c o s (x)})

x \to 5 - lim (\frac{x - 1}{2 x - 10})

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

x \to 0 lim (x - e^{x} + 1)

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