Find the approximate value of (15)^{frac{1}{4 | vedclass

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Question

(A) Let $y = x^{\frac{1}{4}}$. We want to find the approximate value of $(15)^{\frac{1}{4}}$.Choose $x = 16$ and $\Delta x = -1$,since $16$ is the nea

Vedclass · Accepted Answer

$1.96875$

Vedclass · Answer

(A) Let $y = x^{\frac{1}{4}}$. We want to find the approximate value of $(15)^{\frac{1}{4}}$.Choose $x = 16$ and $\Delta x = -1$,since $16$ is the nearest fourth power to $15$.Then $y = (16)^{\frac{1}{4}} = 2$.The differential $dy$ is given by $dy = \frac{dy}{dx} \Delta x$.Since $y = x^{\frac{1}{4}}$,$\frac{dy}{dx} = \frac{1}{4} x^{-\frac{3}{4}} = \frac{1}{4 x^{\frac{3}{4}}}$.At $x = 16$,$\frac{dy}{dx} = \frac{1}{4 (16)^{\frac{3}{4}}} = \frac{1}{4 	imes 8} = \frac{1}{32} = 0.03125$.Thus,$dy = \frac{dy}{dx} \Delta x = 0.03125 	imes (-1) = -0.03125$.The approximate value is $y + dy = 2 + (-0.03125) = 1.96875$.

Find the approximate value of $(15)^{\frac{1}{4}}$.

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