What is the limit as x approaches 1 of (x^2-1)/(1-x^3) ?

The limit as x approaches 1 of (x^2-1)/(1-x^3) is -2/3

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limit as x approaches 1 of (x^2-1)/(1-x^3)

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

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

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

Simplify

= - \frac{2}{3}

x \to 1 lim (cos (2 x))

x \to 2 lim (8 - 3 x)

x \to π lim (10 sin (x))

x \to 2 + lim (e^{x - 2})

x \to \infty lim (\frac{( - 2 ) x ^{3} + x ^{2} + 1}{( - 3 ) x ^{4} + 2 x ^{2} + 1})

What is the limit as x approaches 1 of (x^2-1)/(1-x^3) ?
The limit as x approaches 1 of (x^2-1)/(1-x^3) is -2/3