What is the limit as x approaches-1+of x/(|x+1|) ?

The limit as x approaches-1+of x/(|x+1|) is -infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches-1+of x/(|x+1|)

x \to - 1 + lim (\frac{x}{∣ x + 1 ∣})

- \infty

Solution steps

x \to - 1 + lim (\frac{x}{∣ x + 1 ∣})

x + 1

is positive when

x \to - 1 +

. Therefore

∣ x + 1 ∣ = x + 1

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

Divide by highest denominator power:

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

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

For

x

approaching

- 1

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - \infty

y, y = x e^{y}

\int_{- 3}^{- 2} (2 x (3 - x^{2})^{3}) d x

f (x) = cos (x), at x = π

\frac{e ^{- 4 s}}{s ( s ^{2} + 16 )}

\frac{d y}{d x} = - 3 y

What is the limit as x approaches-1+of x/(|x+1|) ?
The limit as x approaches-1+of x/(|x+1|) is -infinity