Explanation Given Information: Definition of an absolute value function: | f ( x ) | = { f ( x ) a ≤ x ≤ c − f ( x ) c ≤ x ≤ b In a signed function for all values of x the function f ( x ) can take both negative and positive values. Hence the area measured using the definite integral can be count positive as ∫ a c f ( x ) d x or count negative as ∫ c b f ( x ) d x as shown below. In an absolute function for all values of x the function f ( x ) cannot take negative values

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4.6, Problem 10C

To determine

To Explain: the absolute area of a function ∫ab|f(x)|dx counts only area positive

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Chapter 4.6, Problem 9C

Chapter 4.6, Problem 11C

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Chapter 4 Solutions

Calculus

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the absolute area of a function ∫ a b | f ( x ) | d x counts only area positive

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Chapter 4 Solutions