What is the limit as x approaches-2+of (5x)/(2+x) ?

The limit as x approaches-2+of (5x)/(2+x) 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-2+of (5x)/(2+x)

x \to - 2 + lim (\frac{5 x}{2 + x})

- \infty

Solution steps

x \to - 2 + lim (\frac{5 x}{2 + x})

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

= 5 \cdot x \to - 2 + lim (\frac{x}{2 + x})

Divide by highest denominator power:

\frac{1}{\frac{2}{x} + 1}

= 5 \cdot x \to - 2 + lim (\frac{1}{\frac{2}{x} + 1})

For

x

approaching

- 2

from the right

, x > - 2 \Rightarrow \frac{2}{x} + 1 < 0

The denominator is a negative quantity approaching 0 from the left

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

What is the limit as x approaches-2+of (5x)/(2+x) ?
The limit as x approaches-2+of (5x)/(2+x) is -infinity