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

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

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

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

3

Solution steps

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

Simplify

\frac{1 - x ^{3}}{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{( 5 ^{x} - 2 ^{x} )}{x})

x \to \infty lim (- a x)

x \to 0 lim (\frac{6 ^{x} - 3 ^{x}}{x})

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

x \to 1 + lim (x^{\frac{9}{x - 1}})

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