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 + 1 . Find the n th Taylor polynomial of the function f ( x ) = x + 1 at x = 0 , n = 3 as follows by using the above mentioned definition. P 3 ( x ) = f ( 0 ) + f ′ ( 0 ) ( x − 0 ) + f ″ ( 0 ) 2 ! ( x − 0 ) 2 + f ‴ ( 0 ) 3 ! ( x − 0 ) 3 (1) The derivative of f ′ ( x ) is calculated as follows. f ′ ( x ) = d d x ( x + 1 ) = 1 2 x + 1 The derivative of f ″ ( x ) is calculated as follows. f ″ ( x ) = d d x ( 1 2 x + 1 ) = − 1 4 ( x + 1 ) 3 2 The derivative of f ‴ ( x ) is calculated as follows. f ‴ ( x ) = d d x ( − 1 4 ( x + 1 ) 3 2 ) = 3 8 ( x + 1 ) 5 2 When x = 0 , find f ( 0 ) as follows

Applied Calculus for the Managerial, Life, and Social Sciences

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ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.1, Problem 18E

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To find: The nth Taylor polynomial of the function f(x)=x+1 at x=0,n=3.

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Chapter 11.1, Problem 17E

Chapter 11.1, Problem 19E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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 n th Taylor polynomial of the function f ( x ) = x + 1 at x = 0 , n = 3 .

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Chapter 11 Solutions