What is the limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8)) ?

The limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8)) is 1/12

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limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8))

\frac{1}{12}

Decimal Notation

0.08333 \dots

Solution steps

Apply L'Hopital's Rule

: x \to 8 lim (\frac{\frac{1}{3 x ^{\frac{2}{3}}}}{1})

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

Plug in the value

x = 8

= \frac{\frac{1}{3 \cdot 8 ^{\frac{2}{3}}}}{1}

Simplify

\frac{\frac{1}{3 \cdot 8 ^{\frac{2}{3}}}}{1} : \frac{1}{12}

= \frac{1}{12}

\frac{d}{d x} (f (x) e^{\frac{1}{f ( x )}})

f^{^{'}} (x) = \frac{( 5 x ^{2} - 9 x + 8 )}{7 x + 6}

\frac{\partial}{\partial x} (e^{- y})

\int \frac{- x - 1}{x ^{2} + x + 1} d x

\int x^{5} cos (2 x) d x

What is the limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8)) ?
The limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8)) is 1/12