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# Solved: Piecewise Continuous FunctionsAlthough we are ISBN: 9780321884077 57

## Solution for problem 12AAE Chapter 5

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 12AAE

Piecewise Continuous Functions

Although we are mainly interested in continuous functions, many functions in applications are piecewise continuous. A function ƒ(x) is piecewise continuous on a closed interval I if ƒ has only finitely many discontinuities in I, the limits exist and are finite at every interior point of I, and the appropriate onesided limits exist and are finite at the endpoints of I. All piecewise continuous functions are integrable. The points of discontinuity subdivide I into open and half-open subintervals on which ƒ is continuous, and the limit criteria above guarantee that ƒ has a continuous extension to the closure of each subinterval. To integrate a piecewise continuous function, we integrate the individual extensions and add the results. The integral of (Figure 5.32) over [-1, 3] is FIGURE 5.32 Piecewise continuous functions like this are integrated piece by piece.

The Fundamental Theorem applies to piecewise continuous functions with the restriction that is expected to equal ƒ(x) only at values of x at which ƒ is continuous. There is a similar restriction on Leibniz’s Rule (see Exercises 31–38).

Graph the functions and integrate them over their domains. Step-by-Step Solution:

Step 1 of 3</p>

In this problem we have to graph the given functions and integrate them over the given domain.

Given functions and Step 2 of 3</p>

Graph of the given functions given below Step 3 of 3

##### ISBN: 9780321884077

The full step-by-step solution to problem: 12AAE from chapter: 5 was answered by , our top Calculus solution expert on 08/01/17, 02:37PM. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. This full solution covers the following key subjects: Continuous, functions, piecewise, integrate, open. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. The answer to “Piecewise Continuous FunctionsAlthough we are mainly interested in continuous functions, many functions in applications are piecewise continuous. A function ƒ(x) is piecewise continuous on a closed interval I if ƒ has only finitely many discontinuities in I, the limits exist and are finite at every interior point of I, and the appropriate onesided limits exist and are finite at the endpoints of I. All piecewise continuous functions are integrable. The points of discontinuity subdivide I into open and half-open subintervals on which ƒ is continuous, and the limit criteria above guarantee that ƒ has a continuous extension to the closure of each subinterval. To integrate a piecewise continuous function, we integrate the individual extensions and add the results. The integral of (Figure 5.32) over [-1, 3] is FIGURE 5.32 Piecewise continuous functions like this are integrated piece by piece.The Fundamental Theorem applies to piecewise continuous functions with the restriction that is expected to equal ƒ(x) only at values of x at which ƒ is continuous. There is a similar restriction on Leibniz’s Rule (see Exercises 31–38).Graph the functions and integrate them over their domains.” is broken down into a number of easy to follow steps, and 184 words. Since the solution to 12AAE from 5 chapter was answered, more than 233 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13.

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