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 4.7, Problem 2ES
Approximate the following
- a.
- b.
- c.
- d.
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3) Let R be a set of real number and d:R2 R R such that
d((x, y), (z, w)) = √(x-2)² + (y-w)² show that d is a metric on R².H.W
Use a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b).
x-a
f(x)=
1 - cos (4x-4)
3(x-1)²
; a = 1
a. Use a graphing utility to graph f. Select the correct graph below..
A.
W
→
✓
Each graph is displayed in a [- 1,3] by [0,5] window.
B.
in
✓
○ C.
und
☑
Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x-1
○ A. The limit appears to be approximately ☐ .
(Round to the nearest tenth as needed.)
B. The limit does not exist.
b. Evaluate f(x) for values of x near 1 to support your conjecture.
X
0.9
0.99
0.999
1.001
1.01
1.1
f(x)
○ D.
+
☑
(Round to six decimal places as needed.)
Does the table from the previous step support your conjecture?
A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…
x²-19x+90
Let f(x) =
.
Complete parts (a) through (c) below.
x-a
a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
x→a+
○ A.
a=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no values of a for which the limit equals a finite number.
b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A.
(Type integers or simplified fractions)
C. There are no values of a that satisfy lim f(x) = ∞.
+
x-a
c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
x→a+
A. Either a
(Type integers or simplified fractions)
B.
Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Use the forward-difference formulas and...Ch. 4.1 - The data in Exercise 1 were taken from the...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - The data in Exercise 5 were taken from the...Ch. 4.1 - The data in Exercise 6 were taken from the...Ch. 4.1 - Prob. 9ESCh. 4.1 - Use the formulas given in this section to...Ch. 4.1 - The data in Exercise 9 were taken from the...Ch. 4.1 - Prob. 12ES
Ch. 4.1 - Use the following data and the knowledge that the...Ch. 4.1 - Prob. 14ESCh. 4.1 - Prob. 15ESCh. 4.1 - Prob. 16ESCh. 4.1 - Prob. 17ESCh. 4.1 - Prob. 18ESCh. 4.1 - Prob. 19ESCh. 4.1 - Prob. 20ESCh. 4.1 - Prob. 21ESCh. 4.1 - In a circuit with impressed voltage (t) and...Ch. 4.1 - In Exercise 9 of Section 3.4, data were given...Ch. 4.1 - Derive an O(h4) five-point formula to approximate...Ch. 4.1 - Use the formula derived in Exercise 24 and the...Ch. 4.1 - a. Analyze the round-off errors, as in Example 4,...Ch. 4.1 - Derive a method for approximating f (x0) whose...Ch. 4.1 - Consider the function e(h)=h+h26M, where M is a...Ch. 4.1 - Prob. 1DQCh. 4.1 - Prob. 2DQCh. 4.2 - Apply the extrapolation process described in...Ch. 4.2 - Add another line to the extrapolation table in...Ch. 4.2 - The following data give approximations to the...Ch. 4.2 - Prob. 6ESCh. 4.2 - Prob. 7ESCh. 4.2 - The forward-difference formula can be expressed as...Ch. 4.2 - Prob. 9ESCh. 4.2 - Prob. 10ESCh. 4.2 - Prob. 11ESCh. 4.2 - Prob. 12ESCh. 4.2 - Prob. 13ESCh. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Approximate the following integrals using the...Ch. 4.3 - Find a bound for the error in Exercise 1 using the...Ch. 4.3 - Prob. 4ESCh. 4.3 - Repeat Exercise 1 using Simpsons rule. 1....Ch. 4.3 - Prob. 6ESCh. 4.3 - Prob. 7ESCh. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Prob. 10ESCh. 4.3 - Prob. 11ESCh. 4.3 - Prob. 12ESCh. 4.3 - The Trapezoidal rule applied to 02f(x)dx gives the...Ch. 4.3 - Prob. 14ESCh. 4.3 - Approximate the following integrals using formulas...Ch. 4.3 - Prob. 17ESCh. 4.3 - Suppose that the data of Exercise 17 have...Ch. 4.3 - Prob. 19ESCh. 4.3 - Prob. 20ESCh. 4.3 - The quadrature formula...Ch. 4.3 - The quadrature formula...Ch. 4.3 - Find the constants c0, c1, and x1 so that the...Ch. 4.3 - Find the constants x0, x1, and c1 so that the...Ch. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Prob. 27ESCh. 4.3 - Derive Simpsons Three-Eighths rule (the closed...Ch. 4.3 - Prob. 1DQCh. 4.3 - Prob. 2DQCh. 4.4 - Use the Composite Trapezoidal rule with the...Ch. 4.4 - Prob. 2ESCh. 4.4 - Use the Composite Simpsons rule to approximate the...Ch. 4.4 - Prob. 4ESCh. 4.4 - Prob. 5ESCh. 4.4 - Prob. 6ESCh. 4.4 - Prob. 7ESCh. 4.4 - Prob. 8ESCh. 4.4 - Prob. 9ESCh. 4.4 - Prob. 10ESCh. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 11 for the integral 0x2cosxdx. 11....Ch. 4.4 - Determine the values of n and h required to...Ch. 4.4 - Repeat Exercise 13 for the integral 12xlnxdx. 13....Ch. 4.4 - Prob. 15ESCh. 4.4 - Prob. 17ESCh. 4.4 - A car laps a race track in 84 seconds. The speed...Ch. 4.4 - Prob. 19ESCh. 4.4 - Prob. 20ESCh. 4.4 - Prob. 21ESCh. 4.4 - Prob. 23ESCh. 4.4 - Prob. 24ESCh. 4.4 - Prob. 25ESCh. 4.4 - Prob. 26ESCh. 4.4 - Prob. 1DQCh. 4.4 - Prob. 2DQCh. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Use Romberg integration to compute R3, 3 for the...Ch. 4.5 - Prob. 3ESCh. 4.5 - Prob. 4ESCh. 4.5 - Use the following data to approximate 15f(x)dx as...Ch. 4.5 - Prob. 9ESCh. 4.5 - Prob. 10ESCh. 4.5 - Prob. 11ESCh. 4.5 - Romberg integration for approximating 01f(x)dx...Ch. 4.5 - Prob. 15ESCh. 4.5 - Prob. 18ESCh. 4.5 - Prob. 19ESCh. 4.5 - Prob. 1DQCh. 4.5 - Prob. 4DQCh. 4.6 - Prob. 1ESCh. 4.6 - Prob. 2ESCh. 4.6 - Prob. 11ESCh. 4.6 - Prob. 12ESCh. 4.6 - Could Romberg integration replace Simpsons rule in...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Approximate the following integrals using Gaussian...Ch. 4.7 - Repeat Exercise 1 with n = 3. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 3. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 4. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 4. 2. Approximate the...Ch. 4.7 - Repeat Exercise 1 with n = 5. 1. Approximate the...Ch. 4.7 - Repeat Exercise 2 with n = 5. 2. Approximate the...Ch. 4.7 - Describe the differences and similarities between...Ch. 4.7 - Prob. 2DQCh. 4.8 - Prob. 1DQCh. 4.8 - Prob. 2DQCh. 4.8 - Prob. 3DQCh. 4.8 - Prob. 4DQCh. 4.9 - Suppose a body of mass m is traveling vertically...Ch. 4.9 - The Laguerre polynomials {L0(x), L1(x) ...} form...Ch. 4.9 - Prob. 7ESCh. 4.9 - Prob. 8ESCh. 4.9 - Prob. 9ESCh. 4.9 - Prob. 1DQCh. 4.9 - Prob. 2DQ
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