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Chapter 4: Q. 42 (page 404)
Integral Formulas: Fill in the blanks to complete each of the following integration formulas.
The value of.
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Show that is an antiderivative of .
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 the graph of f to estimate the values of A(1), A(2), A(3)
Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value
Suppose f is positive on (鈭掆垶, 鈭�1] and [2,鈭�) and negative on the interval [鈭�1, 2]. Write (a) the signed area and (b) the absolute area between the graph of f and the x-axis on [鈭�3, 4] in terms of definite integrals that do not involve absolute values.
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