What is the limit as x approaches-8+of (-9x)/(x+8) ?

The limit as x approaches-8+of (-9x)/(x+8) is infinity

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limit as x approaches-8+of (-9x)/(x+8)

x \to - 8 + lim (\frac{- 9 x}{x + 8})

\infty

Solution steps

x \to - 8 + lim (\frac{- 9 x}{x + 8})

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

= - 9 \cdot x \to - 8 + lim (\frac{x}{x + 8})

Divide by highest denominator power:

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

= - 9 \cdot x \to - 8 + lim (\frac{1}{1 + \frac{8}{x}})

For

x

approaching

- 8

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - 9 (- \infty)

Apply Infinity Property:

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

= \infty

\frac{d}{d x} (2 x^{2} + 3 x + 2)

\int \frac{1}{x ^{2} - 8 x + 15} d x

(x y + 4 y^{2} + 2 x^{2}) d x - (x^{2}) d y = 0

y = e^{9}

\int + e^{- 3 x} sin (b x) d x

What is the limit as x approaches-8+of (-9x)/(x+8) ?
The limit as x approaches-8+of (-9x)/(x+8) is infinity