15. (a) Find the quadratic approximation for the function f(x) = x3/2 centered at a = 4. (b) Use your answer from part (a) to approximate (4.2)2.

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A: (6) F = Q , (a*b) = ([max(a, b)] /b)  - 9

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A: We will use definition of Laplace transformation to solve this problem.

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A: please comment if you need any clarification. If you find my answer useful please put thumbs up.

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A: All the options has been explained with full detail below.

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A: The solution is given as

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Q: Theorem 1 : If f L[S(c); p] = F(p), then L;P = (u) đu , provided that the integral exists.

A: The solution is given as