What is the limit as x approaches 0 of ((343+x)^{1/3}-7)/x ?

The limit as x approaches 0 of ((343+x)^{1/3}-7)/x is 1/147

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limit as x approaches 0 of ((343+x)^{1/3}-7)/x

x \to 0 lim (\frac{( 343 + x ) ^{\frac{1}{3}} - 7}{x})

\frac{1}{147}

Decimal

0.00680 \dots

Solution steps

x \to 0 lim (\frac{( 343 + x ) ^{\frac{1}{3}} - 7}{x})

Apply L'Hopital's Rule

= x \to 0 lim \frac{\frac{1}{3 ( x + 343 ) ^{\frac{2}{3}}}}{1}

Plug in the value

x = 0

= \frac{\frac{1}{3 ( 0 + 343 ) ^{\frac{2}{3}}}}{1}

Simplify

\frac{\frac{1}{3 ( 0 + 343 ) ^{\frac{2}{3}}}}{1} : \frac{1}{147}

= \frac{1}{147}

What is the limit as x approaches 0 of ((343+x)^{1/3}-7)/x ?
The limit as x approaches 0 of ((343+x)^{1/3}-7)/x is 1/147