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

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

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

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

12

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 8

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

Simplify

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

= 12

\frac{d}{d x} (4 x^{3})

\frac{d}{d x} (x + x^{- 1})

x \to + 0 lim (\frac{3 x}{x e ^{x}})

\frac{\partial}{\partial y} (x^{3} y - y^{4})

\frac{d}{d x} (arcsin (9 x^{4}))

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