Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Textbook Question
Chapter 2.4, Problem 9ES
- a. Construct a sequence that converges to 0 of order 3.
- b. Suppose α > 1. Construct a sequence that converges to 0 of order α.
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Directions: For problems 1 through 3, read each question carefully and be sure to show all work.
1. What is the phase shift for y = 2sin(2x-)?
2. What is the amplitude of y = 7cos(2x+л)?
3. What is the period of y = sin(3x-π)?
Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to
include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift
between the two graphs. Write in complete sentences.
4. y 3sin(2x) and y = 3cos(2x)
5. y 4sin(2x) and y = cos(3x- -플)
A graph G of order 12 has vertex set V(G) = {c1, c2, …, c12} for the twelve configurations inFigure 1.4. A “move” on this checkerboard corresponds to moving a single coin to anunoccupied square, where(1) the gold coin can only be moved horizontally or diagonally,(2) the silver coin can only be moved vertically or diagonally.Two vertices ci and cj (i ≠ j) are adjacent if it is possible to move ci to cj by a single move.
(a) What vertices are adjacent to c1 in G?(c) Draw the subgraph of G induced by {c2, c6, c9, c11}.
i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti-
ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u
you choose to apply to i and j.
(ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do-
ce configurations of figure 1. A movement on said board corresponds to moving a
coin to an unoccupied square using the following two rules:
1. the gold coin can move only horizontally or diagonally,
2. the silver coin can move only vertically or diagonally.
Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement.
a) What vertices are adjacent to c1 in G?
b) Draw the subgraph induced by {c2, c6, c9, c11}
Chapter 2 Solutions
Numerical Analysis
Ch. 2.1 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.1 - Let f(x) = 3(x +1)(x 12)(x 1) = 0. Use the...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Prob. 7ESCh. 2.1 - Prob. 8ESCh. 2.1 - Prob. 9ESCh. 2.1 - Prob. 10ESCh. 2.1 - Prob. 11ES
Ch. 2.1 - Let f(x) = (x + 2)(x + 1)x(x 1)3(x 2). To which...Ch. 2.1 - Find an approximation to 253 correct to within 104...Ch. 2.1 - Find an approximation to 3 correct to within 104...Ch. 2.1 - A trough of length L has a cross section in the...Ch. 2.1 - Use Theorem 2.1 to find a bound for the number of...Ch. 2.1 - Prob. 18ESCh. 2.1 - Prob. 19ESCh. 2.1 - Let f(x) = (x 1)10, p = 1, and pn = 1 + 1/n. Show...Ch. 2.1 - The function defined by f(x) = sin x has zeros at...Ch. 2.1 - Prob. 1DQCh. 2.1 - Prob. 2DQCh. 2.1 - Is the Bisection method sensitive to the starting...Ch. 2.2 - Use algebraic manipulation to show that each of...Ch. 2.2 - a. Perform four iterations, if possible, on each...Ch. 2.2 - Let f(x) = x3 2x + 1. To solve f(x) = 0, the...Ch. 2.2 - Let f(x) = x4 + 3x2 2. To solve f(x) = 0, the...Ch. 2.2 - The following four methods are proposed to compute...Ch. 2.2 - Prob. 6ESCh. 2.2 - Prob. 7ESCh. 2.2 - Prob. 8ESCh. 2.2 - Use Theorem 2.3 to show that g(x) = + 0.5...Ch. 2.2 - Use Theorem 2.3 to show that g(x) = 2x has a...Ch. 2.2 - Use a fixed-point iteration method to find an...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Prob. 20ESCh. 2.2 - Prob. 21ESCh. 2.2 - a. Show that Theorem 2.3 is true if the inequality...Ch. 2.2 - a. Use Theorem 2.4 to show that the sequence...Ch. 2.2 - Prob. 24ESCh. 2.2 - Prob. 25ESCh. 2.2 - Suppose that g is continuously differentiable on...Ch. 2.3 - Let f(x) = x2 6 and p0 = 1. Use Newtons method to...Ch. 2.3 - Let f(x) = x3 cos x and p0 = 1. Use Newtons...Ch. 2.3 - Let f(x) = x2 6. With p0 = 3 and p1 = 2, find p3....Ch. 2.3 - Let f(x) = x3 cos x. With p0 = 1 and p1 = 0, find...Ch. 2.3 - Prob. 11ESCh. 2.3 - Prob. 12ESCh. 2.3 - The fourth-degree polynomial...Ch. 2.3 - Prob. 14ESCh. 2.3 - Prob. 15ESCh. 2.3 - Prob. 16ESCh. 2.3 - Prob. 22ESCh. 2.3 - Prob. 23ESCh. 2.3 - Prob. 24ESCh. 2.3 - Prob. 25ESCh. 2.3 - Prob. 27ESCh. 2.3 - A drug administered to a patient produces a...Ch. 2.3 - Prob. 30ESCh. 2.3 - Prob. 32ESCh. 2.3 - Prob. 1DQCh. 2.3 - Prob. 2DQCh. 2.3 - Prob. 3DQCh. 2.3 - Prob. 4DQCh. 2.4 - Prob. 6ESCh. 2.4 - a. Show that for any positive integer k, the...Ch. 2.4 - Prob. 8ESCh. 2.4 - a. Construct a sequence that converges to 0 of...Ch. 2.4 - Prob. 10ESCh. 2.4 - Prob. 11ESCh. 2.4 - Prob. 12ESCh. 2.4 - Prob. 13ESCh. 2.4 - Prob. 14ESCh. 2.4 - Prob. 1DQCh. 2.4 - Prob. 2DQCh. 2.4 - Prob. 4DQCh. 2.5 - Let g(x) = cos(x 1) and p0(0) = 2. Use...Ch. 2.5 - Prob. 4ESCh. 2.5 - Prob. 5ESCh. 2.5 - Prob. 6ESCh. 2.5 - Use Steffensens method to find, to an accuracy of...Ch. 2.5 - Prob. 8ESCh. 2.5 - Prob. 9ESCh. 2.5 - Use Steffensens method with p0 = 3 to compute an...Ch. 2.5 - Use Steffensens method to approximate the...Ch. 2.5 - Prob. 12ESCh. 2.5 - Prob. 13ESCh. 2.5 - Prob. 14ES
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