Let f (x) = 2x cos(2x) (x 2)2 and x0 = 0. a. Find the third Taylor polynomial P3(x), and
Chapter 1, Problem 1.1.12(choose chapter or problem)
Let f (x) = 2x cos(2x) (x 2)2 and x0 = 0. a. Find the third Taylor polynomial P3(x), and use it to approximate f (0.4). b. Use the error formula in Taylors Theorem to find an upper bound for the error | f (0.4) P3(0.4)|. Compute the actual error. c. Find the fourth Taylor polynomial P4(x), and use it to approximate f (0.4). d. Use the error formula in Taylors Theorem to find an upper bound for the error | f (0.4) P4(0.4)|. Compute the actual error.
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