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