What is the limit as x approaches-2-of (-4x)/(x+2) ?

The limit as x approaches-2-of (-4x)/(x+2) is -infinity

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limit as x approaches-2-of (-4x)/(x+2)

x \to - 2 - lim (\frac{- 4 x}{x + 2})

- \infty

Solution steps

x \to - 2 - lim (\frac{- 4 x}{x + 2})

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

= - 4 \cdot x \to - 2 - lim (\frac{x}{x + 2})

Divide by highest denominator power:

\frac{1}{1 + \frac{2}{x}}

= - 4 \cdot x \to - 2 - lim (\frac{1}{1 + \frac{2}{x}})

For

x

approaching

- 2

from the left

, x < - 2 \Rightarrow 1 + \frac{2}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 4 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int x (3 x - 1)^{10} d x

f (x) = \frac{6 x}{x ^{2} + 5}

\int sin^{3} (11 x) cos^{3} (11 x) d x

\int (9 - x^{2}) d x

f (x) = x + x + 5

What is the limit as x approaches-2-of (-4x)/(x+2) ?
The limit as x approaches-2-of (-4x)/(x+2) is -infinity