What is the limit as x approaches 6-of 1/(x-6) ?

The limit as x approaches 6-of 1/(x-6) is -infinity

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limit as x approaches 6-of 1/(x-6)

x \to 6 - lim (\frac{1}{x - 6})

- \infty

Solution steps

x \to 6 - lim (\frac{1}{x - 6})

For

x

approaching

6

from the left

, x < 6 \Rightarrow x - 6 < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

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What is the limit as x approaches 6-of 1/(x-6) ?
The limit as x approaches 6-of 1/(x-6) is -infinity