What is the limit as x approaches-2-of (-6x)/(x+2) ?

The limit as x approaches-2-of (-6x)/(x+2) is -infinity

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limit as x approaches-2-of (-6x)/(x+2)

x \to - 2 - lim (\frac{- 6 x}{x + 2})

- \infty

Solution steps

x \to - 2 - lim (\frac{- 6 x}{x + 2})

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

= - 6 \cdot x \to - 2 - lim (\frac{x}{x + 2})

Divide by highest denominator power:

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

= - 6 \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

= - 6 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int_{0}^{7} \frac{1}{49 - t ^{2}} d t

\int_{0}^{2} \frac{2 x}{( 1 + x ^{2} ) ^{2}} d x

\int 3 x^{3} 4 x^{4} d x

x \to 1 lim (2 x^{3} - 4 x^{2} + x + 8)

9 x + 4

What is the limit as x approaches-2-of (-6x)/(x+2) ?
The limit as x approaches-2-of (-6x)/(x+2) is -infinity