What is the limit as x approaches-7+of-(8x)/(x+7) ?

The limit as x approaches-7+of-(8x)/(x+7) is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches-7+of-(8x)/(x+7)

x \to - 7 + lim (- \frac{8 x}{x + 7})

\infty

Solution steps

x \to - 7 + lim (- \frac{8 x}{x + 7})

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

= - 8 \cdot x \to - 7 + lim (\frac{x}{x + 7})

Divide by highest denominator power:

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

= - 8 \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

= - 8 (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-7+of-(8x)/(x+7) ?
The limit as x approaches-7+of-(8x)/(x+7) is infinity