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Math Calculus EBK FINITE MATHEMATICS AND CALCULUS WIT

Exercises 15–18 require both the trapezoidal rule and Simpson’s rule. They can be worked without calculator programs if such programs are not available, although they require more calculation than the other problems in this exercise set. Error Analysis The difference between the true value of an integral and the value given by the trapezoidal rule or Simpson’s rule is known as the error. In numerical analysis, the error is studied to determine how large n must be for the error to be smaller than some specified amount. For both rules, the error is inversely proportional to a power of n , the number of subdivisions. In other words, the error is roughly k / n p , where k is a constant that depends on the function and the interval, and p is a power that depends only on the method used. With a little experimentation, you can find out what the power p is for the trapezoidal rule and for Simpson’s rule. 15. (a) Find the exact value of ∫ 0 1 x 4 d x . (b) Approximate the integral in part (a) using the trapezoidal rule with n = 4, 8, 16, and 32. For each of these answers, find the absolute value of the error by subtracting the trapezoidal rule answer from the exact answer found in part (a). (c) If the error is k / n p , then the error times n p should be approximately a constant. Multiply the errors in part (b) times n p for p = 1, 2, etc., until you find a power p yielding the same answer for all four values of n .

Exercises 15–18 require both the trapezoidal rule and Simpson’s rule. They can be worked without calculator programs if such programs are not available, although they require more calculation than the other problems in this exercise set. Error Analysis The difference between the true value of an integral and the value given by the trapezoidal rule or Simpson’s rule is known as the error. In numerical analysis, the error is studied to determine how large n must be for the error to be smaller than some specified amount. For both rules, the error is inversely proportional to a power of n , the number of subdivisions. In other words, the error is roughly k / n p , where k is a constant that depends on the function and the interval, and p is a power that depends only on the method used. With a little experimentation, you can find out what the power p is for the trapezoidal rule and for Simpson’s rule. 15. (a) Find the exact value of ∫ 0 1 x 4 d x . (b) Approximate the integral in part (a) using the trapezoidal rule with n = 4, 8, 16, and 32. For each of these answers, find the absolute value of the error by subtracting the trapezoidal rule answer from the exact answer found in part (a). (c) If the error is k / n p , then the error times n p should be approximately a constant. Multiply the errors in part (b) times n p for p = 1, 2, etc., until you find a power p yielding the same answer for all four values of n .

Solution Summary: The author explains the fundamental theorem of calculus and the trapezoidal rule.

EBK FINITE MATHEMATICS AND CALCULUS WIT

EBK FINITE MATHEMATICS AND CALCULUS WIT

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 15.6, Problem 15E

Exercises 15–18 require both the trapezoidal rule and Simpson’s rule. They can be worked without calculator programs if such programs are not available, although they require more calculation than the other problems in this exercise set.

Error Analysis The difference between the true value of an integral and the value given by the trapezoidal rule or Simpson’s rule is known as the error. In numerical analysis, the error is studied to determine how large n must be for the error to be smaller than some specified amount. For both rules, the error is inversely proportional to a power of n, the number of subdivisions. In other words, the error is roughly k/n^p, where k is a constant that depends on the function and the interval, and p is a power that depends only on the method used. With a little experimentation, you can find out what the power p is for the trapezoidal rule and for Simpson’s rule.

15. (a) Find the exact value of ∫ 0 1 x 4 d x .

(b) Approximate the integral in part (a) using the trapezoidal rule with n = 4, 8, 16, and 32. For each of these answers, find the absolute value of the error by subtracting the trapezoidal rule answer from the exact answer found in part (a).

(c) If the error is k/n^p, then the error times n^p should be approximately a constant. Multiply the errors in part (b) times n^p for p = 1, 2, etc., until you find a power p yielding the same answer for all four values of n.

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Chapter 15.6, Problem 14E

Chapter 15.6, Problem 16E

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Chapter 15 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. 15.1 - Find an antiderivative f(x)=8x7.Ch. 15.1 - Find 1t4dt.Ch. 15.1 - Find (6x2+8x9)dx.Ch. 15.1 - Find x32xdx.Ch. 15.1 - Find (3x+e3x)dx.Ch. 15.1 - Repeat Example 11(b) and 11(c) for the Burj...Ch. 15.1 - Prob. 7YT Ch. 15.1 - Find the derivative of the following functions....Ch. 15.1 - Find the derivative of the following functions....Ch. 15.1 - Prob. 1E

Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - APPLICATIONS Business and Economics Cost Find the...Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Cost Find the cost function for each marginal cost...Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - Prob. 54E Ch. 15.1 - Prob. 55E Ch. 15.1 - Prob. 56E Ch. 15.1 - Prob. 57E Ch. 15.1 - Prob. 58E Ch. 15.1 - Prob. 59E Ch. 15.1 - Prob. 60E Ch. 15.1 - Prob. 61E Ch. 15.1 - Prob. 62E Ch. 15.1 - Cell Growth Under certain conditions, the number...Ch. 15.1 - Prob. 64E Ch. 15.1 - Prob. 65E Ch. 15.1 - Prob. 66E Ch. 15.1 - Prob. 67E Ch. 15.1 - Prob. 68E Ch. 15.1 - Prob. 69E Ch. 15.1 - Prob. 70E Ch. 15.1 - Prob. 71E Ch. 15.1 - Prob. 72E Ch. 15.1 - Prob. 73E Ch. 15.1 - Prob. 74E Ch. 15.2 - Prob. 1YT Ch. 15.2 - Prob. 2YT Ch. 15.2 - Prob. 3YT Ch. 15.2 - Prob. 4YT Ch. 15.2 - Prob. 5YT Ch. 15.2 - Prob. 6YT Ch. 15.2 - Prob. 1WE Ch. 15.2 - Prob. 2WE Ch. 15.2 - Prob. 3WE Ch. 15.2 - Prob. 1E Ch. 15.2 - Prob. 2E Ch. 15.2 - Prob. 3E Ch. 15.2 - Prob. 4E Ch. 15.2 - Prob. 5E Ch. 15.2 - Prob. 6E Ch. 15.2 - Prob. 7E Ch. 15.2 - Prob. 8E Ch. 15.2 - 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Prob. 7E Ch. 15.3 - In Exercises 512, approximate the area under the...Ch. 15.3 - Prob. 9E Ch. 15.3 - Prob. 10E Ch. 15.3 - Prob. 11E Ch. 15.3 - Prob. 12E Ch. 15.3 - Prob. 13E Ch. 15.3 - Prob. 14E Ch. 15.3 - Prob. 15E Ch. 15.3 - Prob. 16E Ch. 15.3 - Prob. 17E Ch. 15.3 - Prob. 18E Ch. 15.3 - Prob. 19E Ch. 15.3 - Prob. 20E Ch. 15.3 - Prob. 21E Ch. 15.3 - Prob. 22E Ch. 15.3 - Prob. 24E Ch. 15.3 - Prob. 25E Ch. 15.3 - Prob. 26E Ch. 15.3 - Prob. 27E Ch. 15.3 - Prob. 28E Ch. 15.3 - Prob. 29E Ch. 15.3 - Prob. 30E Ch. 15.3 - Prob. 31E Ch. 15.3 - Prob. 32E Ch. 15.3 - Prob. 33E Ch. 15.3 - Prob. 34E Ch. 15.3 - Prob. 35E Ch. 15.3 - Prob. 36E Ch. 15.3 - Prob. 37E Ch. 15.3 - Prob. 38E Ch. 15.3 - Prob. 39E Ch. 15.3 - Prob. 40E Ch. 15.4 - Prob. 1YT Ch. 15.4 - Prob. 2YT Ch. 15.4 - Prob. 3YT Ch. 15.4 - Prob. 4YT Ch. 15.4 - Prob. 5YT Ch. 15.4 - Prob. 1WE Ch. 15.4 - Prob. 2WE Ch. 15.4 - Prob. 3WE Ch. 15.4 - Prob. 1E Ch. 15.4 - Prob. 2E Ch. 15.4 - Prob. 3E Ch. 15.4 - Prob. 4E Ch. 15.4 - Prob. 5E Ch. 15.4 - 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Prob. 54E Ch. 15.4 - Prob. 55E Ch. 15.4 - Prob. 56E Ch. 15.4 - Prob. 57E Ch. 15.4 - Prob. 58E Ch. 15.4 - Prob. 59E Ch. 15.4 - Prob. 60E Ch. 15.4 - Prob. 61E Ch. 15.4 - Prob. 62E Ch. 15.4 - Prob. 63E Ch. 15.4 - Prob. 64E Ch. 15.4 - Prob. 65E Ch. 15.4 - Prob. 66E Ch. 15.4 - Beagles The daily energy requirements of female...Ch. 15.4 - Prob. 68E Ch. 15.4 - Prob. 69E Ch. 15.4 - Prob. 70E Ch. 15.4 - Prob. 71E Ch. 15.4 - Prob. 72E Ch. 15.5 - Repeat Example 1 for f(x) = 4 x2, g(x) = x + 2, x...Ch. 15.5 - Prob. 2YT Ch. 15.5 - Repeat Example 3 for y = x2 3x and y = 2x on [0,...Ch. 15.5 - Prob. 4YT Ch. 15.5 - Evaluate each of the following integrals....Ch. 15.5 - Prob. 2WE Ch. 15.5 - Prob. 1E Ch. 15.5 - Prob. 2E Ch. 15.5 - Prob. 3E Ch. 15.5 - Prob. 4E Ch. 15.5 - Prob. 5E Ch. 15.5 - Prob. 6E Ch. 15.5 - Prob. 7E Ch. 15.5 - Prob. 8E Ch. 15.5 - Prob. 9E Ch. 15.5 - Prob. 10E Ch. 15.5 - Prob. 11E Ch. 15.5 - Prob. 12E Ch. 15.5 - Prob. 13E Ch. 15.5 - Prob. 14E Ch. 15.5 - Prob. 15E Ch. 15.5 - Prob. 16E Ch. 15.5 - Prob. 17E Ch. 15.5 - Prob. 18E Ch. 15.5 - Prob. 19E Ch. 15.5 - Prob. 20E Ch. 15.5 - Prob. 21E Ch. 15.5 - Prob. 22E Ch. 15.5 - Prob. 23E Ch. 15.5 - Prob. 24E Ch. 15.5 - Prob. 25E Ch. 15.5 - Prob. 26E Ch. 15.5 - Prob. 27E Ch. 15.5 - Prob. 28E Ch. 15.5 - Prob. 29E Ch. 15.5 - Prob. 30E Ch. 15.5 - Prob. 31E Ch. 15.5 - Prob. 32E Ch. 15.5 - Consumers Surplus Find the consumers surplus if...Ch. 15.5 - Prob. 34E Ch. 15.5 - Consumers and Producers Surplus Suppose the supply...Ch. 15.5 - Consumers and Producers Surplus Suppose the supply...Ch. 15.5 - Consumers and Producers Surplus Suppose that with...Ch. 15.5 - Prob. 38E Ch. 15.5 - Prob. 39E Ch. 15.5 - Prob. 40E Ch. 15.5 - Prob. 41E Ch. 15.5 - Prob. 42E Ch. 15.6 - Prob. 1YT Ch. 15.6 - Prob. 2YT Ch. 15.6 - Prob. 1E Ch. 15.6 - Prob. 2E Ch. 15.6 - Prob. 3E Ch. 15.6 - Prob. 4E Ch. 15.6 - Prob. 5E Ch. 15.6 - Prob. 6E Ch. 15.6 - Prob. 7E Ch. 15.6 - Prob. 8E Ch. 15.6 - Prob. 9E Ch. 15.6 - Prob. 10E Ch. 15.6 - Prob. 11E Ch. 15.6 - Prob. 12E Ch. 15.6 - Prob. 13E Ch. 15.6 - Prob. 14E Ch. 15.6 - Exercises 1518 require both the trapezoidal rule...Ch. 15.6 - Prob. 16E Ch. 15.6 - Prob. 17E Ch. 15.6 - Prob. 18E Ch. 15.6 - Prob. 19E Ch. 15.6 - Prob. 20E Ch. 15.6 - Prob. 21E Ch. 15.6 - Prob. 22E Ch. 15.6 - Prob. 23E Ch. 15.6 - Prob. 24E Ch. 15.6 - Prob. 25E Ch. 15.6 - Prob. 26E Ch. 15.6 - Prob. 27E Ch. 15.6 - Prob. 28E Ch. 15.6 - Prob. 29E Ch. 15.6 - Prob. 30E Ch. 15.6 - Prob. 31E Ch. 15.6 - Prob. 32E Ch. 15.6 - Prob. 33E Ch. 15.6 - Prob. 34E Ch. 15.6 - Prob. 35E Ch. 15 - Determine whether each of the following statements...Ch. 15 - Prob. 2RE Ch. 15 - Prob. 3RE Ch. 15 - Prob. 4RE Ch. 15 - Determine whether each of the following statements...Ch. 15 - Prob. 6RE Ch. 15 - Prob. 7RE Ch. 15 - Prob. 8RE Ch. 15 - Prob. 9RE Ch. 15 - Prob. 10RE Ch. 15 - Prob. 11RE Ch. 15 - Prob. 12RE Ch. 15 - Prob. 13RE Ch. 15 - Prob. 14RE Ch. 15 - Prob. 15RE Ch. 15 - Prob. 16RE Ch. 15 - Prob. 17RE Ch. 15 - Prob. 18RE Ch. 15 - Prob. 19RE Ch. 15 - Prob. 20RE Ch. 15 - Prob. 21RE Ch. 15 - Prob. 22RE Ch. 15 - Prob. 23RE Ch. 15 - Prob. 24RE Ch. 15 - Prob. 25RE Ch. 15 - Prob. 26RE Ch. 15 - Prob. 27RE Ch. 15 - Prob. 28RE Ch. 15 - Prob. 29RE Ch. 15 - Prob. 30RE Ch. 15 - Prob. 31RE Ch. 15 - Prob. 32RE Ch. 15 - Prob. 33RE Ch. 15 - Prob. 34RE Ch. 15 - Prob. 35RE Ch. 15 - Prob. 36RE Ch. 15 - Prob. 37RE Ch. 15 - Prob. 38RE Ch. 15 - Prob. 39RE Ch. 15 - Prob. 40RE Ch. 15 - Prob. 41RE Ch. 15 - Prob. 42RE Ch. 15 - Prob. 43RE Ch. 15 - Prob. 44RE Ch. 15 - Prob. 45RE Ch. 15 - Prob. 46RE Ch. 15 - Prob. 47RE Ch. 15 - Prob. 48RE Ch. 15 - Prob. 49RE Ch. 15 - Prob. 50RE Ch. 15 - Prob. 51RE Ch. 15 - Prob. 52RE Ch. 15 - Prob. 53RE Ch. 15 - Prob. 54RE Ch. 15 - Prob. 55RE Ch. 15 - Prob. 56RE Ch. 15 - Prob. 57RE Ch. 15 - Prob. 58RE Ch. 15 - Prob. 59RE Ch. 15 - Prob. 60RE Ch. 15 - Prob. 61RE Ch. 15 - Prob. 62RE Ch. 15 - Prob. 63RE Ch. 15 - Prob. 64RE Ch. 15 - Prob. 65RE Ch. 15 - Prob. 66RE Ch. 15 - Prob. 67RE Ch. 15 - Prob. 68RE Ch. 15 - Prob. 69RE Ch. 15 - Prob. 70RE Ch. 15 - Prob. 71RE Ch. 15 - Prob. 72RE Ch. 15 - Prob. 73RE Ch. 15 - Prob. 74RE Ch. 15 - Prob. 75RE Ch. 15 - Prob. 76RE Ch. 15 - Prob. 77RE Ch. 15 - Prob. 78RE Ch. 15 - Prob. 79RE Ch. 15 - Prob. 80RE Ch. 15 - Prob. 81RE Ch. 15 - Prob. 82RE Ch. 15 - Sales The rate of change of sales of a new brand...Ch. 15 - Prob. 84RE Ch. 15 - Prob. 85RE Ch. 15 - Prob. 86RE Ch. 15 - QD 87. Oil Production The following table shows...Ch. 15 - Prob. 88RE Ch. 15 - Prob. 89RE Ch. 15 - Prob. 90RE Ch. 15 - Prob. 91RE Ch. 15 - Prob. 92RE Ch. 15 - Prob. 93RE Ch. 15 - Prob. 94RE Ch. 15 - Prob. 95RE

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