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Chapter 4: Q. 47 (page 404)
Integral Formulas: Fill in the blanks to complete each of the
following integration formulas.
(The last six formulas involve hyperbolic functions and their inverses.)
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Describe the intervals on which the function f is positive, negative, increasing and decreasing. Them describe the intervals on which the function A is positive , negative, increasing and decreasing
Shade in the regions between the two functions shown here on the intervals (a) [−2, 3]; (b) [−1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?
Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value
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.
Prove Theorem 4.13(c): For any real numbers a and b, Use the proof of Theorem 4.13(a) as a guide.
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