Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
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Textbook Question
Chapter 2.2, Problem 1E
Use the Bisection method to find
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(b) Let I[y] be a functional of y(x) defined by
[[y] = √(x²y' + 2xyy' + 2xy + y²) dr,
subject to boundary conditions
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y(1) = 1.
State the Euler-Lagrange equation for finding extreme values of I [y] for this prob-
lem. Explain why the function y(x) = x is an extremal, and for this function,
show that I = 2. Without doing further calculations, give the values of I for the
functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
In simplest terms, Sketch the graph of the parabola. Then, determine its equation.
opens downward, vertex is (- 4, 7), passes through point (0, - 39)
Chapter 2 Solutions
Numerical Methods
Ch. 2.2 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.2 - Let f(x)=3(x+1)x12(x1). Use the Bisection method...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Sketch the graphs of y=x and y=2sinx. Use the...Ch. 2.2 - Sketch the graphs of y=x and y=tanx. Use the...Ch. 2.2 - Let f(x)=(x+2)(x+1)x(x1)3(x2). To which zero of f...Ch. 2.2 - Let f(x)=(x+2)(x+1)2x(x1)3(x2). To which zero of f...Ch. 2.2 - Use the Bisection method to find an approximation...Ch. 2.2 - Use the Bisection method to find an approximation...
Ch. 2.2 - Find a bound for the number of Bisection method...Ch. 2.2 - Prob. 12ECh. 2.2 - The function defined by f(x)=sinx has zeros at...Ch. 2.3 - Let f(x)=x26,p0=3, and p1=2. Find p3 using each...Ch. 2.3 - Prob. 2ECh. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Use the Secant method to find all four solutions...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - The fourth-degree polynomial...Ch. 2.3 - The function f(x)=tanx6 has a zero at (1/) arctan...Ch. 2.3 - The sum of two numbers is 20. If each number is...Ch. 2.3 - A trough of length L has a cross section in the...Ch. 2.3 - Prob. 17ECh. 2.4 - Let f(x)=x26 and p0=1. Use Newtons method to find...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Use Newtons method to find all solutions of...Ch. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.5 - The following sequences are linearly convergent....Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.6 - Find the approximations to within 104 to all the...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Repeat Exercise 2 using Mullers method.Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Two ladders crisscross an alley of width W. Each...Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12E
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