What is the limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x ?

The limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x is 1/12

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limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x

\frac{1}{12}

Decimal

0.08333 \dots

Solution steps

Apply L'Hopital's Rule

= x \to 0 lim \frac{\frac{1}{3 ( x + 8 ) ^{\frac{2}{3}}}}{1}

Plug in the value

x = 0

= \frac{\frac{1}{3 ( 0 + 8 ) ^{\frac{2}{3}}}}{1}

Simplify

\frac{\frac{1}{3 ( 0 + 8 ) ^{\frac{2}{3}}}}{1} : \frac{1}{12}

= \frac{1}{12}

What is the limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x ?
The limit as x approaches 0 of (\sqrt[3]{8+x}-\sqrt[3]{8})/x is 1/12