What is the limit as x approaches-8+of (2x)/(x+8) ?

The limit as x approaches-8+of (2x)/(x+8) is -infinity

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limit as x approaches-8+of (2x)/(x+8)

x \to - 8 + lim (\frac{2 x}{x + 8})

- \infty

Solution steps

x \to - 8 + lim (\frac{2 x}{x + 8})

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

= 2 \cdot x \to - 8 + lim (\frac{x}{x + 8})

Divide by highest denominator power:

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

= 2 \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

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

f (x) = \frac{2}{4 x + 3}

f (x) = \frac{1 - 3 x}{1 + 3 x}

x \to \frac{3}{4} lim (\frac{4 x ^{2} - 9}{2 x - 3})

\int_{0}^{3} 3 - x d x

(4 sin (x))^{^{'}}

What is the limit as x approaches-8+of (2x)/(x+8) ?
The limit as x approaches-8+of (2x)/(x+8) is -infinity