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Chapter 4: Q. 08 (page 364)
Preview of Differential Equations:
Given each of the following equations involving a functionf, find a possible formula for f(x).
The possible formula for the function is .
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Prove Theorem 4.13(b): For any real numbers a and b, we have. Use the proof of Theorem 4.13(a) as a guide.
Show by exhibiting a counterexample that, in general, . In other words, find two functions f and g such that the integral of their quotient is not equal to the quotient of their integrals.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: ).
Consider the general sigma notation .What do we mean when we say that ak is a function of k?
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