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Chapter 4: Q. 12 (page 403)
Notation: Describe the meanings of each of the following mathematical expressions or how they are commonly used in this chapter:
.
For any function on an interval , the difference will be called the evaluation of on and will be denoted by,
.
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Suppose f is a function whose average value on is
and whose average rate of change on the same in-
terval is . Sketch a possible graph for f . Illustrate the
average value and the average rate of change on your
graph of f .
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
Compare the definitions of the definite and indefinite integrals. List at least three things that are different about these mathematical objects.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.
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