Let = arctan(a) So X I = (a) Find the Taylor polynomial of order 2, P2(x), about x arctan(2). (b) Use Lagrange's formula for the remainder R₂(x) V 0 arctan(r) X -dx dx. (c) Hence calculate I with an error up to 9' = = 0 for the function arctan(x) - P₂(x) to show that · S² P₁(x) dx | ≤ 1/1/ X 9

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