What is the limit as x approaches-5+of-(9x)/(x+5) ?

The limit as x approaches-5+of-(9x)/(x+5) is infinity

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limit as x approaches-5+of-(9x)/(x+5)

x \to - 5 + lim (- \frac{9 x}{x + 5})

\infty

Solution steps

x \to - 5 + lim (- \frac{9 x}{x + 5})

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

= - 9 \cdot x \to - 5 + lim (\frac{x}{x + 5})

Divide by highest denominator power:

\frac{1}{1 + \frac{5}{x}}

= - 9 \cdot x \to - 5 + lim (\frac{1}{1 + \frac{5}{x}})

For

x

approaching

- 5

from the right

, x > - 5 \Rightarrow 1 + \frac{5}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - 9 (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

What is the limit as x approaches-5+of-(9x)/(x+5) ?
The limit as x approaches-5+of-(9x)/(x+5) is infinity