Use MATLAB to: (a) Approximate the roots of the function f (x) defined by: f(x) = x² sin(x) (b) Calculate the roots of f (x) as defined in part (a) in a span of [-6, 6]. (c) Estimate a function g(x) by deriving the Taylor series of the function (x) up to order 8. (d) Calculate the roots of the Taylor series in the span of [-6, 6].

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A: Here is the matlab code. See below step for code and output.

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A: The requested matlab code is given below with explanatory comments.