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

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

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

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

\infty

Solution steps

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

For

x

approaching

- 3

from the left

, x < - 3 \Rightarrow x^{2} - 9 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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