Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 3.4, Problem 5CP
To determine
To find: The equations and to plot the cubic spline S that satisfying the given data.
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Students have asked these similar questions
A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³.
(a) Find the total profit in the first three years.
(b) Find the profit in the sixth year of operation.
(c) What is happening to the annual profit over the long run?
(a) The total profit in the first three years is $
(Round to the nearest dollar as needed.)
I just need to know why this is wrong below:
What is the test statistic W? W=5 (incorrect)
and
What is the p-value of this test? (p-value < 0.001-- incorrect)
Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages
pages
127
217
486
132
397
297
396
327
292
256
358
272
What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12
Alpha Level
0.001
0.005
0.01
0.025
0.05
0.1
0.2
Critical Value
75
70
68
64
60
56
50
What is the p-value for this test? p-value < 0.001
Find the area between the curves.
x= -2, x = 7, y=2x² +3, y=0
Set up the integral (or integrals) needed to compute this area. Use the smallest possible number
of integrals. Select the correct choice below and fill in the answer boxes to complete your choice.
A.
7
[[2x² +3] dx
-2
B.
[[ ] dx+
-2
7
S [ ] dx
The area between the curves is
(Simplify your answer.)
Chapter 3 Solutions
Numerical Analysis
Ch. 3.1 - Use Lagrange interpolation to find a polynomial...Ch. 3.1 - Use Newtons divided differences to find the...Ch. 3.1 - How many degree d polynomials pass through the...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - (a) Find a polynomial P(x) of degree 3 or less...Ch. 3.1 - Write down a polynomial of degree exactly 5 that...Ch. 3.1 - Find P(0), where P(x) is the degree 10 polynomial...Ch. 3.1 - Let P(x) be the degree 9 polynomial that takes the...Ch. 3.1 - Give an example of the following, or explain why...Ch. 3.1 - Let P(x) be the degree 5 polynomial that takes the...
Ch. 3.1 - Let P1, P2, P3, and P4 be four different points...Ch. 3.1 - Can a degree 3 polynomial intersect a degree 4...Ch. 3.1 - Let P(x) be the degree 10 polynomial through the...Ch. 3.1 - Write down 4 noncollinear points (1,y1), (2,y2),...Ch. 3.1 - Write down the degree 25 polynomial that passes...Ch. 3.1 - List all degree 42 polynomials that pass through...Ch. 3.1 - The estimated mean atmospheric concentration of...Ch. 3.1 - Prob. 18ECh. 3.1 - Apply the following world population figures to...Ch. 3.1 - Write a version of Program 3.2 that is a MATLAB...Ch. 3.1 - Write a MATLAB function polyinterp.m that takes as...Ch. 3.1 - Remodel the sin1 calculator key in Program 3.3 to...Ch. 3.1 - (a) Use the addition formulas for sin and cos to...Ch. 3.2 - Find the degree 2 interpolating polynomial P2(x)...Ch. 3.2 - (a) Given the data points (1,0), (2,In2), (4,In4),...Ch. 3.2 - Assume that the polynomial P9(x) interpolates the...Ch. 3.2 - Consider the interpolating polynomial for...Ch. 3.2 - Assume that a function f(x) has been approximated...Ch. 3.2 - Assume that the polynomial P5(x) interpolates a...Ch. 3.2 - (a) Use the method of divided differences to find...Ch. 3.2 - Plot the interpolation error of the sin1 key from...Ch. 3.2 - The total world oil production in millions of...Ch. 3.2 - Use the degree 3 polynomial through the first four...Ch. 3.3 - List the Chebyshev interpolation nodes x1,...,xn...Ch. 3.3 - Find the upper bound for | (xx1)...(xxn) | on the...Ch. 3.3 - Assume that Chebyshev interpolation is used to...Ch. 3.3 - Answer the same questions as in Exercise 3, but...Ch. 3.3 - Find an upper bound for the error on [ 0,2 ] when...Ch. 3.3 - Assume that you are to use Chebyshev interpolation...Ch. 3.3 - Suppose you are designing the In key for a...Ch. 3.3 - Let Tn(x) denote the degree n Chebyshev...Ch. 3.3 - Determine the following values: (a) T999(1) (b)...Ch. 3.3 - Prob. 1CPCh. 3.3 - Prob. 2CPCh. 3.3 - Carry out the steps of Computer Problem 2 forIn x,...Ch. 3.3 - Let f(x)=e| x |, Compare evenly spaced...Ch. 3.3 - Prob. 5CPCh. 3.4 - Decide whether the equations form a cubic spline....Ch. 3.4 - Check the spline conditions for {...Ch. 3.4 - Find c in the following cubic splines. Which of...Ch. 3.4 - Find k1,k2,k3 in the following cubic spline. Which...Ch. 3.4 - How many natural cubic splines on [ 0,2 ] are...Ch. 3.4 - Find the parabolically terminated cubic spline...Ch. 3.4 - Solve equations 3.26 to find the natural cubic...Ch. 3.4 - Solve equations 3.26 to find the natural cubic...Ch. 3.4 - Prob. 9ECh. 3.4 - True or false: Given n=3 data points, the...Ch. 3.4 - (a) How many parabolically terminated cubic...Ch. 3.4 - How many not-a-knot cubic splines are there for...Ch. 3.4 - Find b1 and c3 in the cubic spline S(x)={...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Discuss the existence and uniqueness of a...Ch. 3.4 - Prob. 21ECh. 3.4 - Prob. 1CPCh. 3.4 - Find and plot the not-a-knot cubic spline that...Ch. 3.4 - Find and plot the cubic spline S satisfying...Ch. 3.4 - Prob. 4CPCh. 3.4 - Prob. 5CPCh. 3.4 - Find and plot the cubic spline S satisfying...Ch. 3.4 - Prob. 7CPCh. 3.4 - Prob. 8CPCh. 3.4 - Find the clamped cubic spline that interpolates...Ch. 3.4 - Find the number of interpolation nodes in Computer...Ch. 3.4 - (a) Consider the natural cubic spline through the...Ch. 3.4 - Prob. 12CPCh. 3.4 - In a single plot, show the natural, not-a-knot,...Ch. 3.4 - Prob. 14CPCh. 3.4 - Prob. 15CPCh. 3.5 - Find the one-piece BĂ©zier curve (x(t),y(t))...Ch. 3.5 - Find the first endpoint two control points, and...Ch. 3.5 - Find the three-piece BĂ©zier curve forming the...Ch. 3.5 - Build a four-piece BĂ©zier spline that forms a...Ch. 3.5 - Describe the character drawn by the following...Ch. 3.5 - Describe the character drawn by the following...Ch. 3.5 - Find a one-piece BĂ©zier spline that has vertical...Ch. 3.5 - Find a one-piece Bezier spline that has a...Ch. 3.5 - Prob. 9ECh. 3.5 - Find the knots and control points for the...Ch. 3.5 - Prove the facts in (3.27), and explain how they...Ch. 3.5 - Given (x1,y1), (x2,y2), (x3,y3), and (x4,y4), show...Ch. 3.5 - Plot the cure in Exercise 7.Ch. 3.5 - Prob. 2CPCh. 3.5 - Plot the letter from BĂ©zier curves: (a) W (b) B...Ch. 3.5 - Use the bezierdraw.m program of Section 3.5 to...Ch. 3.5 - Revise the draw program to accept an n8 matrix of...Ch. 3.5 - Using the template above and your favorite text...Ch. 3.5 - Prob. 4SACh. 3.5 - Although font information was a closely guarded...Ch. 3.5 - Prob. 6SA
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