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

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

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

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

- \infty

Solution steps

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

Simplify

\frac{x - 2}{x ^{2} - 4} : \frac{1}{x + 2}

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

For

x

approaching

- 2

from the left

, x < - 2 \Rightarrow x + 2 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

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

x \to 0 + lim (- 1 + ln (x) x)

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

x \to 4 lim (\frac{x - 4}{4 - x})

x \to 0 lim (\frac{7 ^{x} - 1}{5 x})

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