What is the limit as x approaches 0 of ((2-x)^3-8)/x ?

The limit as x approaches 0 of ((2-x)^3-8)/x is -12

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limit as x approaches 0 of ((2-x)^3-8)/x

x \to 0 lim (\frac{( 2 - x ) ^{3} - 8}{x})

- 12

Solution steps

x \to 0 lim (\frac{( 2 - x ) ^{3} - 8}{x})

Simplify

\frac{( 2 - x ) ^{3} - 8}{x} : - x^{2} + 6 x - 12

= x \to 0 lim (- x^{2} + 6 x - 12)

Plug in the value

x = 0

= - 0^{2} + 6 \cdot 0 - 12

Simplify

= - 12

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What is the limit as x approaches 0 of ((2-x)^3-8)/x ?
The limit as x approaches 0 of ((2-x)^3-8)/x is -12