The approximate value of sqrt[3]{64.04} is | vedclass

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(C) Let $f(x) = x^{1/3}$. We need to find the approximate value of $f(64.04)$.Let $x = 64$ and $\Delta x = 0.04$.Then $f(x + \Delta x) \approx f(x) +

Vedclass · Accepted Answer

$4.00083$

Vedclass · Answer

(C) Let $f(x) = x^{1/3}$. We need to find the approximate value of $f(64.04)$.Let $x = 64$ and $\Delta x = 0.04$.Then $f(x + \Delta x) \approx f(x) + f'(x) \cdot \Delta x$.Here,$f(x) = x^{1/3}$,so $f'(x) = \frac{1}{3} x^{-2/3} = \frac{1}{3(x^{1/3})^2}$.For $x = 64$,$f(64) = 64^{1/3} = 4$.$f'(64) = \frac{1}{3(4)^2} = \frac{1}{3 \cdot 16} = \frac{1}{48}$.Now,$f(64.04) \approx 4 + \frac{1}{48} \cdot 0.04$.$f(64.04) \approx 4 + \frac{0.04}{48} = 4 + \frac{4}{4800} = 4 + \frac{1}{1200}$.$f(64.04) \approx 4 + 0.000833...$Thus,the approximate value is $4.00083$.

The approximate value of $\sqrt[3]{64.04}$ is

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