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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

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

= - 2 \cdot x \to - 6 + lim (\frac{1}{1 + \frac{6}{x}})

For

x

approaching

- 6

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - 2 (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

(0.2) (2)

\frac{d}{d x} (x^{10} e^{x + 1})

\frac{d y}{d t} = y (1 - y), y (0) = 16

\int \frac{t ^{2} - 1}{t ^{4} - 1} d t

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x} \cdot ln (x)

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