Find the radial polynomial p(x, y) a br cr 2 , where r 2 x 2 y 2 , that best approximates the function f(x, y) x using the L 2 norm on the unit disk D r 1 to measure the least squares error

Question: Find the radial polynomial p(x, y) = a + br + cr 2 , where r 2 = x 2 + y 2 , that

Find the radial polynomial p(x, y) = a + br + cr², where r² = x²+ y², that best approximates the function f(x, y) = x using the L² norm on the unit disk D = {r ≤ 1} to measure the least squares error.

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