(A) Explanation Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it is converges otherwise diverges”. Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) ”. Calculation: The rate of the production of an oil well is given by R ( t ) = 1 , 000 t ( 50 + t 2 ) 2 . In order to find total amount of the production of an oil well, its enough to integrate the expression R ( t ) = 1 , 000 t ( 50 + t 2 ) 2 over the interval [ 0 , ∞ ) . That is ∫ 0 ∞ 1 , 000 t ( 50 + t 2 ) 2 d t . Total amount = ∫ 0 ∞ 1 , 000 t ( 50 + t 2 ) 2 d t = 1 , 000 lim b → ∞ ∫ 0 b 1 2 ( 50 + t 2 ) 2 d ( t 2 < (B) To determine To find: The time at which the output of an oil from the well such that it reaches 50% of the total production.

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Author: Stocker

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Chapter 11.1, Problem 68E

(A)

To determine

To find: The total amount of production of an oil well.

(B)

To determine

To find: The time at which the output of an oil from the well such that it reaches 50% of the total production.

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Chapter 11.1, Problem 67E

Chapter 11.1, Problem 69E

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Chapter 11 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The total amount of production of an oil well.

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To find: The total amount of production of an oil well.

To find: The time at which the output of an oil from the well such that it reaches 50% of the total production.

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Chapter 11 Solutions