By Hartmut Laue

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995 5. d]d2. ■ -dkdk+i... 'ofwrighi 2016 ("engage Learning. in whole cr in part. Due to electronie rights, some third party content may he su[pressed from tlx; eBook and/or eChapterfs), Lklilorial review has deemed that any suppressed eonlenldoes not materially afieel the overall learning experience, ("engage Learning reserves the right to remove additional eonlenl at any lime if suhsecjuent rights restrictions recjiireil. didj... dkdk+l ... d[d2... 4+| 4+2 ... d\d2... 1. The numerator is bounded above by 1.

An algorithm is a procedure that describes, in an The use of an algorithm is as old as formal mathematics, but the name derives from the Arabic mathematician Muhammad ibn-Msa al-Khwararizmi (c. 780-850). " unambiguous manner, a finite sequence of steps to be performed in a specified order. The object of the algorithm is to implement a procedure to solve a problem or approximate a solution to the problem. We use a pseudocode to describe the algorithms. This pseudocode specifies the form of the input to be supplied and the form of the desired output.

C. 4). d. 4) |. Compute the actual error. Find the fourth Taylor polynomial /^(x) for the function f {x) — xex~ about xq — 0. a. 4. b. c. Approximate Jj1'4 /(x) dx using J004 P^ix) dx. r0 4 Find an upper bound for the error in (b) using j0' /^(x) dx. d. 2) and find the error. 16. Use the error term of a Taylor polynomial to estimate the error involved in using sinx ^ x to approximate sin 1°. 17. Use a Taylor polynomial about 7r/4 to approximate cos 42° to an accuracy of 10-6. 18. Let /(x) = (1 — x)_1 and Xo = 0.