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

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

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

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 + \frac{9}{x}}

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

For

x

approaching

- 9

from the left

, x < - 9 \Rightarrow 1 + \frac{9}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 6 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\frac{d}{d x} (\frac{x + 3}{x ^{2} + 3})

x = 28 - 7 y^{2}, x = 7 y^{2} - 28

\frac{d y}{d x} = - y^{2}

\frac{d}{d x} (- 5 csc (x) + sec (x))

\frac{d}{d x} (- \frac{12}{( x + 2 ) ^{2}})

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