What is the limit as x approaches 5-of 1/(x^2-25) ?

The limit as x approaches 5-of 1/(x^2-25) is -infinity

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limit as x approaches 5-of 1/(x^2-25)

x \to 5 - lim (\frac{1}{x ^{2} - 25})

- \infty

Solution steps

x \to 5 - lim (\frac{1}{x ^{2} - 25})

For

x

approaching

5

from the left

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

The denominator is a negative quantity approaching 0 from the left

= - \infty

What is the limit as x approaches 5-of 1/(x^2-25) ?
The limit as x approaches 5-of 1/(x^2-25) is -infinity