Explanation Given: The given function is g ( x ) = 4 x . Calculation: Consider the interval to be 1 ≤ t ≤ 1 + h . For h = 0.1 g ′ ( 1 ) ≈ g ( 1.1 ) − g ( 1 ) 1.1 − 1 = [ ( 4 ) 1.1 ] − [ ( 4 ) 1 ] 0.1 = 4.5947 − 4 0.1 = 0.5947 0.1 = 5.947 Thus, the value of g ′ ( 1 ) is 5.947. For h = 0.01 : g ′ ( 1 ) ≈ g ( 1.01 ) − g ( 1 ) 1.01 − 1 = [ ( 4 ) 1

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 2.1, Problem 18P

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Evaluate the value of g′(1) by taking smaller and smaller interval.

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Chapter 2.1, Problem 17P

Chapter 2.1, Problem 19P

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Evaluate the value of g ′ ( 1 ) by taking smaller and smaller interval.

Solution Summary: The author evaluates the value of gprime '(1)' by taking smaller and smaller intervals.

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Evaluate the value of g′(1) by taking smaller and smaller interval.

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Chapter 2 Solutions