Dermine the taylor series expansion for fx through , Mathematics

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Dermine the taylor series expansion for fx through

a. Find the least squares approximation to f(x) = xe^-2x over the interval -1 ≤ x ≤ 1 from the span of 1, x, x² using the stan- dard inner product on C[-1,1].

b. Calculate the error in the approximation using the inner product generated norm.

c. Determine the Taylor series expansion for f(x) through the quadratic term. Calculate the error in this approxi- mation and compare to the error in the least squares approximation.

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