4.18 To calculate a planet's space coordinates, we have to solve the function f(x) = x -1– 0.5 sin x Let the base point be a = x; = T /2 on the interval [0, 1]. Deter- mine the highest-order Taylor series expansion resulting in a maxi- mum error of 0.015 on the specified interval. The error is equal to the absolute value of the difference between the given function and the specific Taylor series expansion. (Hint: Solve graphically.)

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A: Since you have posted multiple questions, according to our guidelines we have done first question…

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Q: Q 3. Find the Taylor series of f at the point c for : (a) f(x) = e", c= 2 (c) f(x) = sin x, c= T (b)…

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