Explanation Definition used: 1. “If f is continuous on ( − ∞ , c ] , then ∫ − ∞ c f ( x ) d x = lim b → − ∞ ∫ b c f ( x ) d x .” 2. “If f is continuous on [ c , ∞ ) , then ∫ c ∞ f ( x ) d x = lim b → ∞ ∫ c b f ( x ) d x .” 3. Let a function f be continuous over the unbounded interval ( − ∞ , ∞ ) . Let c be any real number, and suppose that both the improper integral ∫ − ∞ c f ( x ) d x and ∫ c ∞ f ( x ) d x are convergent. Then the improper integral of f over ( − ∞ , ∞ ) is defined as ∫ − ∞ ∞ f ( x ) d x = ∫ − ∞ c f ( x ) d x + ∫ c ∞ f ( x ) d x , If anyone of the right hand side is divergent then ∫ − ∞ ∞ x d x is divergent. Calculation: The given improper integral is ∫ − ∞ ∞ x 3 ( 1 + x 4 ) − 2 d x . The integrand f ( x ) = x 3 is infinite on the interval of integration ( − ∞ , ∞ ) . In order to find the above integral, first evaluate the ∫ − ∞ 0 x 3 ( 1 + x 4 ) − 2 d x and ∫ 0 ∞ x 3 ( 1 + x 4 ) − 2 d x . By using the above mentioned definition 1 the improper integral is calculated as follows, ∫ − ∞ 0 x 3 ( 1 + x 4 ) − 2 d x = lim b → − ∞ ∫ b 0 x 3 ( 1 + x 4 ) − 2 d x = lim b → − ∞ 1 4 ∫ b 0 ( 1 + x 4 ) − 2 d ( x 4 ) = 1 4 lim b → − ∞ [ 1 1 + x 4 ] b 0 = 1 4 lim b → − ∞ [

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

10th Edition

ISBN: 9781285464640

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 7.4, Problem 39E

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Chapter 7.4, Problem 38E

Chapter 7.4, Problem 40E

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Chapter 7 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Ch. 7.1 - Write the formula for integration by parts.Ch. 7.1 - Explain how you would choose u and dv when using...Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E

Ch. 7.1 - Prob. 9E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 26E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - In Exercises 29-34, evaluate each definite...Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Find the function f given that the slope of the...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Production of Steam Coal In keeping with the...Ch. 7.1 - Prob. 41E Ch. 7.1 - Concentration of a Drug in the Bloodstream The...Ch. 7.1 - Prob. 43E Ch. 7.1 - Average price of a Commodity The price of a...Ch. 7.1 - Distance Covered by a Car The velocity of the...Ch. 7.1 - Credit Card Losses in the United Kingdom The mail...Ch. 7.1 - U.S. Smartphone Users Smartphone users, as a...Ch. 7.1 - Prob. 49E Ch. 7.1 - Future Value of AN Investment Laura, the sole...Ch. 7.1 - Rate of Return on an Investment Suppose an...Ch. 7.1 - Present Value of A Franchise Tracy purchased a...Ch. 7.1 - Gini Index Refer to Section 6.7. The income...Ch. 7.1 - Prob. 56E Ch. 7.1 - A Mixture Problem Two tanks are connected in...Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - Prob. 62E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Producers' SURPLUS for WOMEN'S Boots Refer to...Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.3 - Explain why n can be odd or even in the...Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - In Exercises 23-28, find a bound on the error in...Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Condominium Resort Complex Cooper Realty is...Ch. 7.3 - AVERAGE Temperature The graph depicted ill the...Ch. 7.3 - Surface area of the Jacqueline Kennedy Onassis...Ch. 7.3 - Fuel Consumption of Domestic Cars Thanks to...Ch. 7.3 - Prob. 34E Ch. 7.3 - Medical Costs for Veterans According to a study by...Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Consumers Surplus Refer to Section 6.7. 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The...Ch. 7.5 - The Fountains OF Bellagio Refer to Example 4. The...Ch. 7.5 - Prob. 52E Ch. 7.5 - Reaction Time Of A Motorist The amount of time (in...Ch. 7.5 - Prob. 54E Ch. 7.5 - Prob. 55E Ch. 7.5 - Prob. 56E Ch. 7.5 - Prob. 57E Ch. 7.5 - Prob. 59E Ch. 7.5 - Prob. 60E Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Prob. 63E Ch. 7.5 - Prob. 64E Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 68E Ch. 7.5 - Prob. 69E Ch. 7.5 - Prob. 70E Ch. 7 - Fill in the blanks. 1. The integration by parts...Ch. 7 - Prob. 2CRQ Ch. 7 - Prob. 3CRQ Ch. 7 - Prob. 4CRQ Ch. 7 - Prob. 5CRQ Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Oil Spills Using aerial photographs, the Coast...Ch. 7 - Surface area OF a Lake a man-made lake located in...Ch. 7 - Prob. 40RE Ch. 7 - Prob. 1BM Ch. 7 - Prob. 2BM Ch. 7 - Prob. 3BM Ch. 7 - Prob. 4BM Ch. 7 - Prob. 5BM Ch. 7 - Prob. 6BM

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The given improper integral, whenever it is convergent.

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Chapter 7 Solutions