13) Suppose you've been tasked with solving the equation ex – 3x – 2 = cos(x) Given that there are both exponential, polynomial, and trigonometric parts, we cannot directly algebraically solve for x. a) Determine the 2nd order Taylor polynomial associated with each non-polynomial term in the equation. Show all work. b) Replace each non-polynomial term with its approximating Taylor polynomial. c) Determine the exact solution to the resulting polynomial equation – these should be approximate solutions to the original equation. Show work. d) Compare your approximated answers to the decimal solutions of the original equation found in Desmos (or equivalent).
13) Suppose you've been tasked with solving the equation ex – 3x – 2 = cos(x) Given that there are both exponential, polynomial, and trigonometric parts, we cannot directly algebraically solve for x. a) Determine the 2nd order Taylor polynomial associated with each non-polynomial term in the equation. Show all work. b) Replace each non-polynomial term with its approximating Taylor polynomial. c) Determine the exact solution to the resulting polynomial equation – these should be approximate solutions to the original equation. Show work. d) Compare your approximated answers to the decimal solutions of the original equation found in Desmos (or equivalent).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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