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Chapter 4: Q. 8 (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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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. (Hint for Exercise 54: ).
Explain why at this point we don’t have an integration formula for the function whereas we do have an integration formula for .
Approximate the same area as earlier but this time with eight rectangles is this over approximation or under approximation of the exact area under the graph
Properties of addition: State the associative law for addition, the commutative law for addition, and the distributive law for multiplication over addition of real numbers. (You may have to think back to a previous algebra course.)
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