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

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

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

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

- \infty

Solution steps

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

Divide by highest denominator power:

\frac{1}{1 + \frac{6}{x}}

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

For

x

approaching

- 6

from the right

, x > - 6 \Rightarrow 1 + \frac{6}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

x \to 2 lim (3 x^{2} + 4)

x \to 5 - lim (\frac{- 3}{x - 5})

x \to 1 lim (3 x - 2)

x \to 3 - lim (\frac{2 x}{9 - x ^{2}})

x \to 3 + lim (\frac{2}{3 - x})

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