What is the limit as x approaches-8-of (-5x)/(x+8) ?

The limit as x approaches-8-of (-5x)/(x+8) is -infinity

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limit as x approaches-8-of (-5x)/(x+8)

x \to - 8 - lim (\frac{- 5 x}{x + 8})

- \infty

Solution steps

x \to - 8 - lim (\frac{- 5 x}{x + 8})

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

= - 5 \cdot x \to - 8 - lim (\frac{x}{x + 8})

Divide by highest denominator power:

\frac{1}{1 + \frac{8}{x}}

= - 5 \cdot x \to - 8 - lim (\frac{1}{1 + \frac{8}{x}})

For

x

approaching

- 8

from the left

, x < - 8 \Rightarrow 1 + \frac{8}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - 5 \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

\int_{3}^{9} (1 + x^{2}) d x

\int \frac{24}{( x - 2 ) ( x ^{2} + 4 )} d x

\int_{0}^{1} \frac{x ^{2}}{x ^{3} - 1} d x

y = e^{5 x}

ln (cos (x))

What is the limit as x approaches-8-of (-5x)/(x+8) ?
The limit as x approaches-8-of (-5x)/(x+8) is -infinity