What is the limit as x approaches 3-of (x-5)/(x^2-9) ?

The limit as x approaches 3-of (x-5)/(x^2-9) is infinity

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limit as x approaches 3-of (x-5)/(x^2-9)

x \to 3 - lim (\frac{x - 5}{x ^{2} - 9})

\infty

Solution steps

x \to 3 - lim (\frac{x - 5}{x ^{2} - 9})

\frac{x - 5}{x ^{2} - 9} = (x - 5) \frac{1}{x ^{2} - 9}

= x \to 3 - lim ((x - 5) \frac{1}{x ^{2} - 9})

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

x \to 3 - lim (x - 5) = - 2

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

= (- 2) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches 3-of (x-5)/(x^2-9) ?
The limit as x approaches 3-of (x-5)/(x^2-9) is infinity