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$Use differential to approximate (27.3)^{1 / 3}$

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2.011

3.1112

3.0111

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detailed solution

Correct option is D

Let y=x1/3dydx=13x−2/3 =13x2/3y+Δy=(x+Δx)1/3Δy=(x+Δx)1/3−x1/3=dydx⋅Δx(x+Δx)1/3=x1/3+13x2/3Δx=(27)1/3=+13(27)2/3(0.3)=3+190=3+0.111110=3.0111

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Use differential to approximate (27.3)1/3

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$Use differential to approximate (27.3)^{1 / 3}$