Find the approximate value of (0.0037)^{frac{ | vedclass

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Question

(A) Let $y = x^{\frac{1}{2}}$.We choose $x = 0.0036$ and $\Delta x = 0.0001$ such that $x + \Delta x = 0.0037$.Then $\Delta y = (x + \Delta x)^{\frac{

Vedclass · Accepted Answer

$0.06083$

Vedclass · Answer

(A) Let $y = x^{\frac{1}{2}}$.We choose $x = 0.0036$ and $\Delta x = 0.0001$ such that $x + \Delta x = 0.0037$.Then $\Delta y = (x + \Delta x)^{\frac{1}{2}} - x^{\frac{1}{2}} = (0.0037)^{\frac{1}{2}} - (0.0036)^{\frac{1}{2}} = (0.0037)^{\frac{1}{2}} - 0.06$.So,$(0.0037)^{\frac{1}{2}} = 0.06 + \Delta y$.We know that $dy \approx \Delta y$,where $dy = \left(\frac{dy}{dx}ight) \Delta x$.Since $y = x^{\frac{1}{2}}$,$\frac{dy}{dx} = \frac{1}{2\sqrt{x}}$.Thus,$dy = \frac{1}{2\sqrt{0.0036}} 	imes 0.0001 = \frac{1}{2 	imes 0.06} 	imes 0.0001 = \frac{0.0001}{0.12} = \frac{1}{1200} \approx 0.000833$.Therefore,$(0.0037)^{\frac{1}{2}} \approx 0.06 + 0.000833 = 0.060833$.

Find the approximate value of $(0.0037)^{\frac{1}{2}}$.

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