What is the limit as x approaches 2-of (x-3)/(x^2-4) ?

The limit as x approaches 2-of (x-3)/(x^2-4) is infinity

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limit as x approaches 2-of (x-3)/(x^2-4)

x \to 2 - lim (\frac{x - 3}{x ^{2} - 4})

\infty

Solution steps

x \to 2 - lim (\frac{x - 3}{x ^{2} - 4})

\frac{x - 3}{x ^{2} - 4} = (x - 3) \frac{1}{x ^{2} - 4}

= x \to 2 - lim ((x - 3) \frac{1}{x ^{2} - 4})

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 2 - lim (x - 3) \cdot x \to 2 - lim (\frac{1}{x ^{2} - 4})

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

x \to 2 - lim (\frac{1}{x ^{2} - 4}) = - \infty

= (- 1) (- \infty)

Apply Infinity Property:

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

= \infty

x \to - 5 lim (x - 8)

x \to - 2 lim (x^{3} - 2 x^{2} + 4 x - 8)

x \to \infty lim (\frac{3 e ^{x} - 4}{5 e ^{x} + 2})

x \to 0 + lim (x arctan (\frac{1}{x}))

x \to 0 lim (5 x + 3)

What is the limit as x approaches 2-of (x-3)/(x^2-4) ?
The limit as x approaches 2-of (x-3)/(x^2-4) is infinity