What is the limit as x approaches 3-of (x+1)/(x^2-9) ?

The limit as x approaches 3-of (x+1)/(x^2-9) is -infinity

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limit as x approaches 3-of (x+1)/(x^2-9)

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

- \infty

Solution steps

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

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

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

x \to 3 - lim (x + 1) = 4

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

= 4 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 2 - lim (x^{2} - 4 x + 1)

x \to \frac{π}{4} lim (\frac{1}{2} cos (x))

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

x \to 0 lim (\frac{x ^{2} + 4 x - 5 - 5}{x})

x \to 1 lim (x^{c s c (π) x})

What is the limit as x approaches 3-of (x+1)/(x^2-9) ?
The limit as x approaches 3-of (x+1)/(x^2-9) is -infinity