So how many terms should I use in getting a certain pre-determined accuracy in a Taylor series. One way is to use the formula for the Taylor’s theorem remainder and its bounds to calculate the number of terms. This is shown in the example below.
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Author: Autar Kaw
Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.
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The Numerical Methods Guy 
I feel this article is very good……. It’s not only interesting; it helps us readers to ponder on the subject. I m very impressed with your work, and I look forward for more of it…. Congratulations on your good work….
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Where does the magic ‘h’ variable come from?
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The magic h is part of the Taylor series. See http://numericalmethods.eng.usf.edu/mws/gen/01aae/mws_gen_aae_spe_taylorseries.pdf for details.
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May I take in you example h as 100 or 1000?
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