Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 5.4, Problem 4CP
Carry out the steps of Computer Problem 1 for the adaptive Midpoint Rule, developed in Exercise 3.
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Question 12
For each function, state whether it is linear.
Function 1
Function 2
{(-1, 5), (0, 10), (1, 17), (2, 25)}
{(2, 2), (4, 4), (6, 8), (8, 16)}
OLinear
ONot linear
OLinear
ONot linear
Function 3
Function 4
-4
-4
-2
-9
-5
4
-14
4
-8
-19
8
-5
OLinear
OLinear
ONot linear
ONot linear
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Soalan / Question 6
y = f(x)
B
Rajah / Figure 2
Rajah 2 menunjukkan lengkung y = f(x) yang ditakrifkan untuk x > 0. Lengkung
tersebut mempunyai titik minimum di A dan melintasi paksi-x di B dan C. Diberi bahawa
= 2x – dan lengkung itu melalui titik
Figure 2 shows the curve y = f(x) defined for x > 0. The curve has a minimum point
at A and crosses the x-axis at B and C. It is given that = 2x – and that the curve
passes through the point (4,).
189
dx
dy
189
16
a) Cari koordinat-x bagi A.
Find the x-coordinate of A.
b) Cari f(x).
Find f(x).
c) Cari koordinat-x bagi B dan C.
Find the x-coordinates of B and C.
d) Cari luas kawasan berlorek.
Find the area of the shaded region.
A certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula
T(W)=aW+(bW+c)p,
where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?
Chapter 5 Solutions
Numerical Analysis
Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Use the three-point centered-difference formula to...Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Carry out the steps of Exercise 3, using the...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Develop a formula for a two-point...Ch. 5.1 - Prove the second-order formula for the first...Ch. 5.1 - Develop a second-order formula for the first...Ch. 5.1 - Find the error term and order formula for the...
Ch. 5.1 - Find a second-order formula for approximating by...Ch. 5.1 - (a) Compute the two-point forward-difference...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Extrapolate the formula developed in Exercise...Ch. 5.1 - Develop a first-order method for approximating ...Ch. 5.1 - Apply extrapolation to the formula developed in...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Find, an upper bound for the error of the machine...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prob. 21ECh. 5.1 - This exercise justifies the beam equations (2.33)...Ch. 5.1 - Use Taylor expansions to prove that (5.16) is a...Ch. 5.1 - Prob. 24ECh. 5.1 - Investigate the reason for the name extrapolation....Ch. 5.1 - Make a table of the error of the three-point...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Prob. 4CPCh. 5.1 - Prob. 5CPCh. 5.2 - Apply the composite Trapezoid Rule with , , and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, , and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Prob. 7ECh. 5.2 - Apply the open Newton-Cotes Rule (5.28) to...Ch. 5.2 - Apply Simpson’s Rule approximation to, and show...Ch. 5.2 - Integrate Newton’s divided-difference...Ch. 5.2 - Find the degree of precision of the following...Ch. 5.2 - Prob. 12ECh. 5.2 - Develop a composite version of the rule (5.28),...Ch. 5.2 - Prove the Composite Midpoint Rule (5.27).
Ch. 5.2 - Find the degree of precision of the degree four...Ch. 5.2 - Use the fact that the error term of Boole’s Rule...Ch. 5.2 - Prob. 17ECh. 5.2 - Prob. 1CPCh. 5.2 - Prob. 2CPCh. 5.2 - Prob. 3CPCh. 5.2 - Prob. 4CPCh. 5.2 - Prob. 5CPCh. 5.2 - Prob. 6CPCh. 5.2 - Apply the Composite Midpoint Rule to the improper...Ch. 5.2 - The arc length of the curve defined by from to ...Ch. 5.2 - Prob. 9CPCh. 5.2 - Prob. 10CPCh. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prove formula (5.31).
Ch. 5.3 - Prove formula (5.35).
Ch. 5.3 - Use Romberg Integration approximation to...Ch. 5.3 - Use Romberg Integration to approximate the...Ch. 5.3 - (a) Test the order of the second column of Romberg...Ch. 5.4 - Apply Adaptive Quadrature by hand, using the...Ch. 5.4 - Apply Adaptive Quadrature by hand, using Simpson’s...Ch. 5.4 - Prob. 3ECh. 5.4 - Develop an Adaptive Quadrature method for rule...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Modify the MATLAB code for Adaptive Trapezoid Rule...Ch. 5.4 - Carry out the steps of Computer Problem 1 for...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Carry out the steps of Problem 6, using Adaptive...Ch. 5.4 - The probability within standard deviations of the...Ch. 5.4 - Write a MATLAB function called myerf.m that uses...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 2ECh. 5.5 - Approximate the integrals in Exercise 1, using ...Ch. 5.5 - Change variables, using the substitution (5.46) to...Ch. 5.5 - Approximate the integrals in Exercise 4, using ...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 7ECh. 5.5 - Find the Legendre polynomials up to degree 3 and...Ch. 5.5 - Prob. 9ECh. 5.5 - Verify the coefficients and in Table 5.1 for...Ch. 5.5 - Write a MATLAB function that uses Adaptive...Ch. 5.5 - Write a program that, for any input between 0 and...Ch. 5.5 - Equipartition the path of Figure 5.6 into ...Ch. 5.5 - Prob. 4SACh. 5.5 - Prob. 5SACh. 5.5 - Prob. 6SACh. 5.5 - Write a program that traverses the path according...
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