What is the limit as x approaches 1 of (1-x)/(x^3-1) ?

The limit as x approaches 1 of (1-x)/(x^3-1) is -1/3

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 (1-x)/(x^3-1)

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

- \frac{1}{3}

Decimal

- 0.33333 \dots

Solution steps

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

Simplify

\frac{1 - x}{x ^{3} - 1} : - \frac{1}{x ^{2} + x + 1}

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

Plug in the value

x = 1

= - \frac{1}{1 ^{2} + 1 + 1}

Simplify

= - \frac{1}{3}

x \to \infty lim (\frac{x}{30})

x \to 0 lim (\frac{1 2 ^{x} - 1 3 ^{x}}{x})

x \to 0 lim (\frac{sin ( 10 x )}{sin ( 8 x )})

x \to 0 lim ((cos (x))^{(\frac{1}{x})^{2}})

x \to - \infty lim (- 2^{x} - 7)

What is the limit as x approaches 1 of (1-x)/(x^3-1) ?
The limit as x approaches 1 of (1-x)/(x^3-1) is -1/3