The approximate value of (0.007)^{frac{1}{3}} | vedclass

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(A) Let $f(x) = x^{\frac{1}{3}}$. We need to find the value of $f(0.007)$.Let $x = 0.008$ and $\Delta x = -0.001$, so that $x + \Delta x = 0.007$.The

Vedclass · Accepted Answer

$0.191$

Vedclass · Answer

(A) Let $f(x) = x^{\frac{1}{3}}$. We need to find the value of $f(0.007)$.Let $x = 0.008$ and $\Delta x = -0.001$, so that $x + \Delta x = 0.007$.The formula for linear approximation is $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.Here, $f(x) = x^{\frac{1}{3}}$, so $f'(x) = \frac{1}{3} x^{-\frac{2}{3}} = \frac{1}{3 x^{\frac{2}{3}}}$.For $x = 0.008$, $f(0.008) = (0.008)^{\frac{1}{3}} = 0.2$.$f'(0.008) = \frac{1}{3(0.008)^{\frac{2}{3}}} = \frac{1}{3(0.04)} = \frac{1}{0.12} = \frac{100}{12} = \frac{25}{3} \approx 8.333$.Now, $f(0.007) \approx 0.2 + (8.333)(-0.001) = 0.2 - 0.008333 = 0.191667$.The closest value among the options is $0.191$.

The approximate value of $(0.007)^{\frac{1}{3}}$ is

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