Explanation Given: Given expressions are 2 − 1 and 101 − 100 . Formula Used: The estimated value of f ( x 0 + 1 ) − f ( x 0 ) at a point x = x 0 is given by f ( x 0 + 1 ) − f ( x 0 ) = f ′ ( x 0 ) …..(1) Calculation: For the actual value of 2 − 1 and 101 − 100 use the above mentioned formula. Here, let us take f ( x ) = x Differentiating both sides with respect to x, we get f ′ ( x ) = 1 2 x Put x 0 = 1 in equation (1). f ( 1 + 1 ) − f ( 1 ) = f ' ( 1 ) 2 − 1 = 1 2 1 2 − 1 = 1 2 2 − 1 = 0.5 Hence the actual value of 2 − 1 is 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 3.4, Problem 39E

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To estimate the value of 2−1 and 101−100. Compare the result with actual value.

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Chapter 3.4, Problem 38E

Chapter 3.4, Problem 40E

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Chapter 3 Solutions

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To estimate the value of 2 − 1 and 101 − 100 . Compare the result with actual value.

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