Find the approximate value of (3.968)^{frac{3 | vedclass

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Question

(A) Let $y = x^{\frac{3}{2}}$.Consider $x = 4$ and $\Delta x = -0.032$.Then,$\Delta y = (x + \Delta x)^{\frac{3}{2}} - x^{\frac{3}{2}} = (3.968)^{\fra

Vedclass · Accepted Answer

$7.904$

Vedclass · Answer

(A) Let $y = x^{\frac{3}{2}}$.Consider $x = 4$ and $\Delta x = -0.032$.Then,$\Delta y = (x + \Delta x)^{\frac{3}{2}} - x^{\frac{3}{2}} = (3.968)^{\frac{3}{2}} - (4)^{\frac{3}{2}} = (3.968)^{\frac{3}{2}} - 8$.So,$(3.968)^{\frac{3}{2}} = 8 + \Delta y$.Now,$dy$ is approximately equal to $\Delta y$,given by $dy = \left(\frac{dy}{dx}\right) \Delta x$.Since $y = x^{\frac{3}{2}}$,we have $\frac{dy}{dx} = \frac{3}{2} x^{\frac{1}{2}}$.Thus,$dy = \frac{3}{2} (4)^{\frac{1}{2}} (-0.032) = \frac{3}{2} (2) (-0.032) = 3 (-0.032) = -0.096$.Therefore,the approximate value is $8 + (-0.096) = 7.904$.

Find the approximate value of $(3.968)^{\frac{3}{2}}$.

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