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

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

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

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

- \infty

Solution steps

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

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

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

x \to 3 - lim (x - 2) = 1

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (arccsc (- 3 x))

\frac{d}{d x} (arctan (\frac{t}{x}))

\frac{d}{d x} (\frac{2 x - 4}{3 e ^{x}})

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

\int 2 x e^{- 2 x^{2}} d x

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