Explanation Definition used: The nth Taylor Polynomial: Let f be a function and its first n derivatives are defined at a. Then the n th Taylor polynomial of f at a is the polynomial, P n ( x ) = f ( a ) + f ′ ( a ) ( x − a ) + f ″ ( a ) 2 ! ( x − a ) 2 + ⋯ + f ( n ) ( a ) n ! ( x − a ) n . Calculation: It is given that the registrar of Kellogg University estimates that the total student enrollment in the Continuing Education division is N ( t ) = − 20 , 000 1 + 0.2 t + 21 , 000 , where N ( t ) denotes the number of students enrolled in the division t years from now. The function is given by N ( t ) = − 20 , 000 1 + 0.2 t + 21 , 000 . Find the second Taylor polynomial of the function N ( t ) = − 20 , 000 1 + 0.2 t + 21 , 000 at t = 0 as follows by using the above mentioned definition. P n ( x ) = f ( a ) + f ′ ( a ) ( x − a ) + f ″ ( a ) 2 ! ( x − a ) 2 + ⋯ + f ( n ) ( a ) n ! ( x − a ) n (1) Let N ( t ) = − 20 , 000 1 + 0.2 t + 21 , 000 . The derivative of N ′ ( t ) is calculated as follows. N ′ ( t ) = 20 , 000 ( 1 + 0.2 t ) 3 2 The derivative of N ″ ( t ) is calculated as follows. N ″ ( t ) = − 600 ( 1 + 0.2 t ) 5 2 When t = 0 , find N ( 0 ) as follows. N ( 0 ) = − 20 , 000 1 + 0.2 ( 0 ) + 21 , 000 = − 20 , 000 + 21 , 000 = 1000 When t = 0 , find N ′ ( 0 ) as follows

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.1, Problem 41E

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To approximate: The average enrollment at Kellogg University between t=0 and t=2 by using the second Taylor polynomial of N(t)=−20,0001+0.2t+21,000.

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Chapter 11.1, Problem 40E

Chapter 11.1, Problem 42E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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To approximate: The average enrollment at Kellogg University between t = 0 and t = 2 by using the second Taylor polynomial of N ( t ) = − 20 , 000 1 + 0.2 t + 21 , 000 .

Solution Summary: The author calculates the average enrollment at Kellogg University by using the second Taylor polynomial of N(t)=-20,000sqrt

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To approximate: The average enrollment at Kellogg University between t=0 and t=2 by using the second Taylor polynomial of N(t)=−20,0001+0.2t+21,000.

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Chapter 11 Solutions