What is the limit as x approaches 0 of (((x+64)^{1/3}-4))/x ?

The limit as x approaches 0 of (((x+64)^{1/3}-4))/x is 1/48

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limit as x approaches 0 of (((x+64)^{1/3}-4))/x

x \to 0 lim \frac{( ( x + 64 ) ^{\frac{1}{3}} - 4 )}{x}

\frac{1}{48}

Decimal Notation

0.02083 \dots

Solution steps

x \to 0 lim (\frac{( x + 64 ) ^{\frac{1}{3}} - 4}{x})

Apply L'Hopital's Rule

: x \to 0 lim \frac{\frac{1}{3 ( x + 64 ) ^{\frac{2}{3}}}}{1}

= x \to 0 lim \frac{\frac{1}{3 ( x + 64 ) ^{\frac{2}{3}}}}{1}

Plug in the value

x = 0

= \frac{\frac{1}{3 ( 0 + 64 ) ^{\frac{2}{3}}}}{1}

Simplify

\frac{\frac{1}{3 ( 0 + 64 ) ^{\frac{2}{3}}}}{1} : \frac{1}{48}

= \frac{1}{48}

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What is the limit as x approaches 0 of (((x+64)^{1/3}-4))/x ?
The limit as x approaches 0 of (((x+64)^{1/3}-4))/x is 1/48