Find the value of (127)^{1/3} up to four deci | vedclass

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(A) Let $y = x^{1/3}$,where $x = 125$ and $x + \Delta x = 127$. Then $\Delta x = 2$. The derivative is $\frac{dy}{dx} = \frac{1}{3x^{2/3}}$. For $x =

Vedclass · Accepted Answer

$5.0267$

Vedclass · Answer

(A) Let $y = x^{1/3}$,where $x = 125$ and $x + \Delta x = 127$. Then $\Delta x = 2$. The derivative is $\frac{dy}{dx} = \frac{1}{3x^{2/3}}$. For $x = 125$,$y = (125)^{1/3} = 5$ and $\frac{dy}{dx} = \frac{1}{3(125)^{2/3}} = \frac{1}{3(25)} = \frac{1}{75}$. Using the approximation $\Delta y \approx \frac{dy}{dx} \cdot \Delta x$,we get $\Delta y \approx \frac{1}{75} 	imes 2 = \frac{2}{75} = 0.02666... \approx 0.0267$. Therefore,$(127)^{1/3} = y + \Delta y = 5 + 0.0267 = 5.0267$.

Find the value of $(127)^{1/3}$ up to four decimal places.

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