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

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

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limit as x approaches 5-of-2/(sqrt(5-x))

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

- \infty

Solution steps

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

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

= - 2 \cdot x \to 5 - lim (\frac{1}{5 - x})

For

x

approaching

5

from the left

, x < 5 \Rightarrow 5 - x > 0

The denominator is a positive quantity approaching 0 from the right

= - 2 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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