What is the limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5} ?

The limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5} is 75

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limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5}

x \to 125 lim (\frac{x - 125}{3 x - 5})

75

Solution steps

x \to 125 lim (\frac{x - 125}{3 x - 5})

Apply L'Hopital's Rule

: x \to 125 lim (\frac{1}{\frac{1}{3 x ^{\frac{2}{3}}}})

= x \to 125 lim (\frac{1}{\frac{1}{3 x ^{\frac{2}{3}}}})

Plug in the value

x = 125

= \frac{1}{\frac{1}{3 \cdot 12 5 ^{\frac{2}{3}}}}

Simplify

\frac{1}{\frac{1}{3 \cdot 12 5 ^{\frac{2}{3}}}} : 75

= 75

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What is the limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5} ?
The limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5} is 75