Explanation Definition used: The Remainder of a Taylor Series If p n is the n th-degree Taylor polynomial for f , then the remainder is R n ( x ) = f ( x ) − p n ( x ) . The error in the approximation f ( x ) ≈ p n ( x ) is | f ( x ) − p n ( x ) | = | R n ( x ) | . Calculation: Consider the equation p 2 ( x ) = 4 − 3 x + 2 x 2 . Substitute x = 0.2 in p 2 ( x ) = 4 − 3 x + 2 x 2 , p 2 ( 0.2 ) = 4 − 3 ( 0.2 ) + 2 ( 0.2 ) 2 = 4 − 0.6 + 0.08 = 3.48 Substitute x = 0

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Chapter 10.4, Problem 8E

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To find: The error in the approximation of f(x)=4−3x+2x2+x3 by p2(x)=4−3x+2x2 at x=0.2.

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Chapter 10.4, Problem 7E

Chapter 10.4, Problem 9E

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The error in the approximation of f ( x ) = 4 − 3 x + 2 x 2 + x 3 by p 2 ( x ) = 4 − 3 x + 2 x 2 at x = 0.2 .

Solution Summary: The author calculates the error in the approximation of f(x)=4-3x+2x

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To find: The error in the approximation of f(x)=4−3x+2x2+x3 by p2(x)=4−3x+2x2 at x=0.2.

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Chapter 10 Solutions