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

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

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

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

- \infty

Solution steps

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

Simplify

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

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

For

x

approaching

- 2

from the right

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

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \to 1 lim (1 - 2 x)

x \to a lim (6 x^{2} - 3 x + 2)

x \to 0 lim (3 x + 1 - 1)

x \to 3 lim (3 x - 2)

x \to \infty lim (x^{k})

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