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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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 81E
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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).
Transcribed Image Text: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).
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