Explanation Given: The given logarithmic value is ln 0.4 Calculation: The graph can be drawn as The function is f ( x ) = 1 t The left-sum defined for n rectangles on [a, b] is = ∑ k = 1 n f ( x k − 1 ) Δ x where, Δ x = b − a n , x k = a + k Δ x Now, Δ x = 0.4 − 0 4 Δ x = 0.1 Therefore, x k = 0 + k ( 1 ) x k = k In the left sum, x k − 1 is the leftmost point in the interval [ x k − 1 , x k ] That is why, x k − 1 = k − 1 The left sum is, = ∑ k = 1 10 ln ( k − 1 ) ( 1 ) = ln ( 0 ) + ln ( 1 ) + ln ( 2 ) + ln ( 3 ) + ln ( 4 ) + ln ( 5 ) + ln ( 6 ) + ln ( 7 ) + ln ( 8 ) + ln ( 9 ) = 1

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.7, Problem 56S

To determine

The logarithmic value using an over-approximation and under approximation

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Chapter 4.7, Problem 55S

Chapter 4.7, Problem 57S

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Chapter 4 Solutions

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The logarithmic value using an over-approximation and under approximation

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