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

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

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

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

- 3

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

= - 1^{2} - 1 - 1

Simplify

= - 3

x \to 0 - lim (\frac{1 + x}{1 - x})

x \to 2 - lim (5)

x \to 7 - lim (\frac{x + 2}{x + 7})

x \to 0 lim (- \frac{9}{x})

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

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