What is the limit as x approaches-9-of (-2x)/(x+9) ?

The limit as x approaches-9-of (-2x)/(x+9) is -infinity

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limit as x approaches-9-of (-2x)/(x+9)

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

- \infty

Solution steps

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

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

= - 2 \cdot x \to - 9 - lim (\frac{x}{x + 9})

Divide by highest denominator power:

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

= - 2 \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

= - 2 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int 2 x^{3} + 5 x^{2} - 2 x + 1 d x

f (x) = \frac{4}{x}, at x = \frac{1}{9}

\int 16 x ln (5 x) d x

\frac{\partial}{\partial x} (x (x^{2} + y^{2})^{- 1})

f (x) = 4 x cos (x)

What is the limit as x approaches-9-of (-2x)/(x+9) ?
The limit as x approaches-9-of (-2x)/(x+9) is -infinity