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

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

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

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

- 3

Solution steps

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

Simplify

\frac{1 - x ^{3}}{x - 1} : - 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 - \infty lim (\frac{2 - 3 e ^{- x}}{5 e ^{- x} - 4})

x \to \infty lim (\frac{x}{e ^{- x}})

x \to 1 lim (\frac{π}{x - 1})

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

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

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