Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Chapter A.5, Problem 15P
Program Plan Intro
Program Description: Purpose of the problem is to show that second Picard approximation is
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Realize the following approximation of the sin(x) function..
sin x ~
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i=0
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x5 x7
+
3! 5! 7!
The approximation is based on the Maclaurin series expansion, and it
becomes an equality (i.e. not only an approximation) as the summation
continues to infinity. Your program will check if the approximation error
falls below 1e-15, and stops if so. Otherwise, it will continue to a
maximum of 100 summations. Your program should ask the user about
the angle (in radians) which they want to find the sin() of. Notice that
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Use the following definition for the approximation error:
Error = abs(true value - approximation) / true value
Hint: you need two loops, where one goes through the summation,
and the other is dedicated to calculating the factorials.
Hint: The angle must be expressed in radians and must be in the
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Q2/apply Gauss Elimination method to solve the equation?
x + 4y -z = -5
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Consider the function f(x) = 1 3x+1 . We approximate f(x) by the Lagrange interpolating polynomial P₂ (x) at the points xo = 1, x₁ = 1.5 and.x₂ = 2. A bound of the theoretical error of this approximation at x = 1.8 is:
Chapter A Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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