Chapter 7: Q. 3 (page 655)
Dominance Relationships for Sequences: Order the following sequences by dominance when
The required order of dominance sequence is
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
Explain why a function a(x) has to be continuous in order for us to use the integral test to analyze a series for convergence.
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
Given thatand, find the value ofrole="math" localid="1648828803227" .
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?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
