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

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

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

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

12

Solution steps

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

Simplify

\frac{( x - 2 ) ^{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

x \to 1 lim (2 - 2 1 - x)

x \to 0 lim (\frac{x}{ln ( 2 x )})

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

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

x \to \frac{3}{2} lim (x + 1)

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