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Chapter 4: Q. 10 (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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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
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 .
Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = on ?
Approximations and limits: Describe in your own words how the slope of a tangent line can be approximated by the slope of a nearby secant line. Then describe how the derivative of a function at a point is defined as a limit of slopes of secant lines. What is the approximation/limit situation described in this section?
Use integration formulas to solve each integral in Exercises 21–62. 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.
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