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

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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}

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