What is the limit as x approaches 0 of ((x-1)^3+1)/x ?

The limit as x approaches 0 of ((x-1)^3+1)/x is 3

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limit as x approaches 0 of ((x-1)^3+1)/x

x \to 0 lim (\frac{( x - 1 ) ^{3} + 1}{x})

3

Solution steps

x \to 0 lim (\frac{( x - 1 ) ^{3} + 1}{x})

Simplify

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

= x \to 0 lim (x^{2} - 3 x + 3)

Plug in the value

x = 0

= 0^{2} - 3 \cdot 0 + 3

Simplify

= 3

What is the limit as x approaches 0 of ((x-1)^3+1)/x ?
The limit as x approaches 0 of ((x-1)^3+1)/x is 3