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 ) = 1 1 − x . The derivatives are f ′ ( x ) = 1 ( 1 − x ) 2 , f ″ ( x ) = 2 ( 1 − x ) 3 and f ‴ ( x ) = 6 ( 1 − x ) 4 . When x = 2 , find f ( 2 ) as follows. f ( 2 ) = 1 1 − 2 = 1 − 1 = − 1 When x = 2 , find f ′ ( 2 ) as follows. f ′ ( 2 ) = 1 ( 1 − 2 ) 2 = 1 1 = 1 When x = 2 , find f ″ ( 2 ) as follows. f ″ ( 2 ) = 2 ( 1 − 2 ) 3 = − 2 1 = − 2 When x = 2 , find f ‴ ( 2 ) as follows. f ‴ ( 2 ) = 6 ( 1 − 2 ) 4 = 6 1 = 6 Find the Taylor polynomial P 1 at x = 2 as follows. P 1 ( x ) = f ( 2 ) + f ′ ( 2 ) ( x − 2 ) = − 1 + 1 ( x − 2 ) = − 1 + ( x − 2 ) Find the Taylor polynomial P 2 at x = 2 as follows

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 11.1, Problem 4E

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To find: The first three Taylor polynomial of the function f(x)=11−x at x=2.

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Chapter 11.1, Problem 3E

Chapter 11.1, Problem 5E

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Chapter 11 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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 ) = 1 1 − x at x = 2 .

Solution Summary: The author explains the first three Taylor polynomials of the function f(x)=11.

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To find: The first three Taylor polynomial of the function f(x)=11−x at x=2.

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Chapter 11 Solutions