What is the limit as x approaches-8+of x/(x+8) ?

The limit as x approaches-8+of x/(x+8) is -infinity

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limit as x approaches-8+of x/(x+8)

x \to - 8 + lim (\frac{x}{x + 8})

- \infty

Solution steps

x \to - 8 + lim (\frac{x}{x + 8})

Divide by highest denominator power:

\frac{1}{1 + \frac{8}{x}}

= x \to - 8 + lim (\frac{1}{1 + \frac{8}{x}})

For

x

approaching

- 8

from the right

, x > - 8 \Rightarrow 1 + \frac{8}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

What is the limit as x approaches-8+of x/(x+8) ?
The limit as x approaches-8+of x/(x+8) is -infinity