What is the limit as x approaches-4-of (-6x)/(x+4) ?

The limit as x approaches-4-of (-6x)/(x+4) is -infinity

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limit as x approaches-4-of (-6x)/(x+4)

x \to - 4 - lim (\frac{- 6 x}{x + 4})

- \infty

Solution steps

x \to - 4 - lim (\frac{- 6 x}{x + 4})

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

= - 6 \cdot x \to - 4 - lim (\frac{x}{x + 4})

Divide by highest denominator power:

\frac{1}{1 + \frac{4}{x}}

= - 6 \cdot x \to - 4 - lim (\frac{1}{1 + \frac{4}{x}})

For

x

approaching

- 4

from the left

, x < - 4 \Rightarrow 1 + \frac{4}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 6 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches-4-of (-6x)/(x+4) ?
The limit as x approaches-4-of (-6x)/(x+4) is -infinity