COMPUTATIONAL METHODS (MEEN3332) Homework#2 Dr. Bouchaib Zazoum, MEC. COE Truncation Errors and the Taylor Series 4.1 Th

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Computational Methods Meen3332 Homework 2 Dr Bouchaib Zazoum Mec Coe Truncation Errors And The Taylor Series 4 1 Th 1 (39.98 KiB) Viewed 24 times

COMPUTATIONAL METHODS (MEEN3332) Homework#2 Dr. Bouchaib Zazoum, MEC. COE Truncation Errors and the Taylor Series 4.1 The following infinite series can be used to approximate e 23! (a) Prove that this Maclaurin series expansion is a special case of the Taylor series expansion [(Eq. (4.7)] with x = 0 and h= x. (b) Use the Taylor series to estimate /(x) eat x1 for x,-0.2. Employ the zero-, first-, for each case. second-, and third-order versions and compute 4.2 The Maclaurin series expansion for cos x is cos.x = 1- 81 Starting with the simplest version, cos x=1, add terms one at a time to estimate cos(7/6). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures.