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: The function is given by f ( x ) = x . The derivatives are f ′ ( x ) = 1 2 x , f ″ ( x ) = − 1 4 x 3 2 and f ‴ ( x ) = 3 8 x 5 2 . When x = 4 , find f ( 4 ) as follows. f ( 4 ) = 4 = 2 When x = 4 , find f ′ ( 4 ) as follows. f ′ ( 4 ) = 1 2 4 = 1 2 ( 2 ) = 1 4 When x = 4 , find f ″ ( 4 ) as follows. f ″ ( 4 ) = − 1 4 ( 4 ) 3 2 = − 1 4 ( 4 ) 3 = − 1 4 ( 2 ) 3 = − 1 32 When x = 4 , find f ‴ ( 4 ) as follows. f ‴ ( 4 ) = 3 8 ( 4 ) 5 2 = 3 8 ( 4 ) 5 = 3 8 ( 2 ) 5 = 3 256 Find the Taylor polynomial P 1 at x = 4 as follows. P 1 ( x ) = f ( 4 ) + f ′ ( 4 ) ( x − 4 ) = 2 + 1 4 ( x − 4 ) Find the Taylor polynomial P 2 at x = 4 as follows

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 11.1, Problem 8E

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To find: The first three Taylor polynomial of the function f(x)=x at x=4.

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Chapter 11.1, Problem 7E

Chapter 11.1, Problem 9E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

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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The first three Taylor polynomial of the function f ( x ) = x at x = 4 .

Solution Summary: The author explains the first three Taylor polynomials of the function f(x)=sqrtx

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To find: The first three Taylor polynomial of the function f(x)=x at x=4.

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Chapter 11 Solutions