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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}}}})

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

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