What is the limit as x approaches 2-of-1/(x^2-4) ?

The limit as x approaches 2-of-1/(x^2-4) is infinity

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limit as x approaches 2-of-1/(x^2-4)

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

\infty

Solution steps

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

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

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

For

x

approaching

2

from the left

, x < 2 \Rightarrow x^{2} - 4 < 0

The denominator is a negative quantity approaching 0 from the left

= - (- \infty)

Simplify

= \infty

What is the limit as x approaches 2-of-1/(x^2-4) ?
The limit as x approaches 2-of-1/(x^2-4) is infinity