Chapter 7: Q. 3 (page 639)
Let be a nonzero polynomial function. Evaluate
Short Answer
If then the value of
Chapter 7: Q. 3 (page 639)
Let be a nonzero polynomial function. Evaluate
If then the value of
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Get started for freeUse either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
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→∞.
(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?
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31–48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
Find the values of x for which the series converges.
Whenever a certain ball is dropped, it always rebounds to a height60% of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of 1 meter?
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