What is the limit as x approaches-6-of (-9x)/(x+6) ?

The limit as x approaches-6-of (-9x)/(x+6) is -infinity

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limit as x approaches-6-of (-9x)/(x+6)

x \to - 6 - lim (\frac{- 9 x}{x + 6})

- \infty

Solution steps

x \to - 6 - lim (\frac{- 9 x}{x + 6})

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

= - 9 \cdot x \to - 6 - lim (\frac{x}{x + 6})

Divide by highest denominator power:

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

= - 9 \cdot x \to - 6 - lim (\frac{1}{1 + \frac{6}{x}})

For

x

approaching

- 6

from the left

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

The denominator is a positive quantity approaching 0 from the right

= - 9 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int_{- \infty}^{0} e^{3 x} d x

\int \frac{1}{u - 1} d u

\int_{10}^{5} 3 x d x

(- 6, 9), (7, - 9)

\frac{\partial}{\partial x} (x ln (x + 2 y + 3 z))

What is the limit as x approaches-6-of (-9x)/(x+6) ?
The limit as x approaches-6-of (-9x)/(x+6) is -infinity