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Find approximation value of (3.968)^(3/2...

Find approximation value of `(3.968)^(3/2)` using differentials.

Text Solution

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`f(x)=f(a)+(x-a)f'(a)`
`f(x)=(4-x)^(3/2)`
`f(0)=f(a)+(-a)f'(a)`
`f'(x)=3/2(4-x)^(1/2)*(-1)`
`=-3/2(4-x)^(1/2)`
`f'(a)=0.032`
`=-3/2(4-0.032)^(1/2)`
`=-3/2*2=-3`
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