Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Question
Chapter 4.1, Problem 16ES
a.
To determine
To fill: The missing entries in the given table using four digit rounding arithmetic and to compare the error with error in 7.
b.
To determine
To fill: The missing entries in the given table using four digit rounding arithmetic and to compare the error with error in 7.
c.
To determine
To fill: The missing entries in the given table using four digit rounding arithmetic and to compare the error with error in 7.
d.
To determine
To fill: The missing entries in the given table using four digit rounding arithmetic and to compare the error with error in 7.
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The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.
a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions.
b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
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after
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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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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardIf a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required when the permissible error is E.arrow_forwardThe analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?arrow_forward
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