Explanation The demand equation for the Tempus sports watch is given by p = 50 e − 0.1 ( x + 1 ) 2 , where x is the quantity demanded per week and p is the unit wholesale price in dollars. Approximate the integrand by a sixth-degree Taylor polynomial about x = − 1 . Find the Taylor series of the function e − 0.1 ( x + 1 ) 2 as follows. 50 e − 1 10 ( x + 1 ) 2 = 50 [ 1 − ( x + 1 ) 2 10 + ( x + 1 ) 4 2 ! ( 100 ) − ( x + 1 ) 6 3 ! ( 1000 ) ] = 50 − 5 ( x + 1 ) 2 + ( x + 4 ) 4 4 − ( x + 1 ) 6 120 It is given that the equilibrium quantity is 1689 units and the unit wholesale price is p = 10 + 5 x 2 . The formula for consumer surplus is given by ∫ 0 x ¯ ( P − p ¯ ) d x , where p ¯ = 10 + 5 x 2 and x ¯ = 1.687 , where x in units of a thousand. Find the consumer’s surplus ∫ 0 1.689 ( 50 e − 0.1 ( x + 1 ) 2 − ( 10 + 5 x 2 ) ) d x by using by a sixth-degree Taylor polynomial. ∫ 0 1.689 ( 50 e − 0.1 ( x + 1 ) 2 − ( 10 + 5 x 2 ) ) d x = { ∫ 0 1

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.6, Problem 32E

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To find: The consumer’s surplus by using a Taylor polynomial approximation of p=f(x)=50e−0.1(x+1)2.

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Chapter 11.6, Problem 31E

Chapter 11.7, Problem 1CQ

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The consumer’s surplus by using a Taylor polynomial approximation of p = f ( x ) = 50 e − 0.1 ( x + 1 ) 2 .

Solution Summary: The author approximate the integrand by a sixth-degree Taylor polynomial about x=-1 to find the consumer's surplus.

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To find: The consumer’s surplus by using a Taylor polynomial approximation of p=f(x)=50e−0.1(x+1)2.

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Chapter 11 Solutions