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Chapter 7: Q. 10 (page 655)
Fill in the blanks to complete each of the following theorem statements.
Basic Limit Rules for Convergent Sequences: If and if c is any constant,
If {mk} and {Mk} are convergent sequences that both converge to L, and if
The required answer is
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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?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31鈥�48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
Consider the series
Fill in the blanks and select the correct word:
An Improper Integral and Infinite Series: Sketch the function for x 鈮� 1 together with the graph of the terms of the series Argue that for every term of the sequence of partial sums for this series,. What does this result tell you about the convergence of the series?
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