What is the limit as x approaches-7+of ((-6x))/(x+7) ?

The limit as x approaches-7+of ((-6x))/(x+7) is infinity

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limit as x approaches-7+of ((-6x))/(x+7)

x \to - 7 + lim (\frac{( - 6 x )}{x + 7})

\infty

Solution steps

x \to - 7 + lim (\frac{- 6 x}{x + 7})

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

= - 6 \cdot x \to - 7 + lim (\frac{x}{x + 7})

Divide by highest denominator power:

\frac{1}{1 + \frac{7}{x}}

= - 6 \cdot x \to - 7 + lim (\frac{1}{1 + \frac{7}{x}})

For

x

approaching

- 7

from the right

, x > - 7 \Rightarrow 1 + \frac{7}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - 6 (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-7+of ((-6x))/(x+7) ?
The limit as x approaches-7+of ((-6x))/(x+7) is infinity