Chapter 7: Q 46. (page 615)
Given thatand, find the value of.
Short Answer
The value ofis 9.
Chapter 7: Q 46. (page 615)
Given thatand, find the value of.
The value ofis 9.
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Get started for freeLet 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish returning each year as , where h is the number of fish whose spawn she releases from the hatchery annually.
(a) Show that the sustained number of fish returning in even-numbered years approach approximately
(Hint: Make a new recurrence by using two steps of the one given.)
(b) Show that the sustained number of fish returning in odd-numbered years approaches approximately
(c) How should Leila choose h, the number of hatchery fish to breed in order to hold the minimum number of fish returning in each run near some constant P?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
Letand be two convergent geometric series. If b and v are both nonzero, prove that is a geometric series. What condition(s) must be met for this series to converge?
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