Find the approximate value of (82)^{frac{1}{4 | vedclass

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Question

(A) Let $y = x^{\frac{1}{4}}$.Consider $x = 81$ and $\Delta x = 1$.Then $y = (81)^{\frac{1}{4}} = 3$.We know that $\Delta y \approx dy = \left(\frac{d

Vedclass · Accepted Answer

$3.009$

Vedclass · Answer

(A) Let $y = x^{\frac{1}{4}}$.Consider $x = 81$ and $\Delta x = 1$.Then $y = (81)^{\frac{1}{4}} = 3$.We know that $\Delta y \approx dy = \left(\frac{dy}{dx}ight) \Delta x$.Since $y = x^{\frac{1}{4}}$,we have $\frac{dy}{dx} = \frac{1}{4} x^{-\frac{3}{4}} = \frac{1}{4 x^{\frac{3}{4}}}$.Substituting the values,$dy = \frac{1}{4(81)^{\frac{3}{4}}} 	imes 1 = \frac{1}{4(3^4)^{\frac{3}{4}}} = \frac{1}{4(3^3)} = \frac{1}{4 	imes 27} = \frac{1}{108}$.Calculating the value,$dy \approx 0.00926$.Thus,$(82)^{\frac{1}{4}} = y + \Delta y \approx 3 + 0.00926 = 3.00926$.Rounding to three decimal places,the approximate value is $3.009$.

Find the approximate value of $(82)^{\frac{1}{4}}$.

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