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Chapter 7: Q. 48 (page 592)
Write each of the arithmetic sequences in Exercises 47鈥�50 in the form
The required form is
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In Exercises 48鈥�51 find all values of p so that the series converges.
Leila, in her capacity as a population biologist in Idaho, is trying to figure out how many salmon a local hatchery should release annually in order to revitalize the fishery. She knows that ifsalmon spawn in Redfish Lake in a given year, then only fish will return to the lake from the offspring of that run, because of all the dams on the rivers between the sea and the lake. Thus, if she adds the spawn from h fish, from a hatchery, then the number of fish that return from that run k will be .
(a) Show that the sustained number of fish returning approaches as k鈫掆垶.
(b) Evaluate .
(c) How should Leila choose h, the number of hatchery fish to raise in order to hold the number of fish returning in each run at some constant P?
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
The contrapositive: What is the contrapositive of the implication 鈥淚f A, then B.鈥�?
Find the contrapositives of the following implications:
If a quadrilateral is a square, then it is a rectangle.
Find the values of x for which the series converges.
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