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 (- \infty)

Apply Infinity Property:

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

= - \infty

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

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

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

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

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

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