What is the limit as x approaches-5-of (-2)/(x^2-25) ?

The limit as x approaches-5-of (-2)/(x^2-25) is -infinity

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limit as x approaches-5-of (-2)/(x^2-25)

x \to - 5 - lim (\frac{- 2}{x ^{2} - 25})

- \infty

Solution steps

x \to - 5 - lim (\frac{- 2}{x ^{2} - 25})

For

x

approaching

- 5

from the left

, x < - 5 \Rightarrow x^{2} - 25 > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

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What is the limit as x approaches-5-of (-2)/(x^2-25) ?
The limit as x approaches-5-of (-2)/(x^2-25) is -infinity