What is the limit as x approaches-1+of x/(1-x^4) ?

The limit as x approaches-1+of x/(1-x^4) 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-1+of x/(1-x^4)

x \to - 1 + lim (\frac{x}{1 - x ^{4}})

- \infty

Solution steps

x \to - 1 + lim (\frac{x}{1 - x ^{4}})

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

\frac{x}{1 - x ^{4}} = \frac{x}{x ^{4} ( \frac{1}{x ^{4}} - 1 )}

= x \to - 1 + lim (\frac{x}{x ^{4} ( \frac{1}{x ^{4}} - 1 )})

Cancel the common factor:

x

= x \to - 1 + lim (\frac{1}{x ^{3} ( \frac{1}{x ^{4}} - 1 )})

For

x

approaching

- 1

from the right

, x > - 1 \Rightarrow x^{3} (\frac{1}{x ^{4}} - 1) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

What is the limit as x approaches-1+of x/(1-x^4) ?
The limit as x approaches-1+of x/(1-x^4) is -infinity