What is the limit as x approaches 8 of ((x^{1/3}-2))/(x-8) ?

The limit as x approaches 8 of ((x^{1/3}-2))/(x-8) is 1/12

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limit as x approaches 8 of ((x^{1/3}-2))/(x-8)

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

\frac{1}{12}

Decimal

0.08333 \dots

Solution steps

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

Apply L'Hopital's Rule

= 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}

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