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Chapter 6: Q. 53 (page 512)
Consider the region between the graphs of and on For each line of rotation given in Exercises 51鈥�54, use definite integrals to find the volume of the resulting solid.
The volume of the solid is
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Suppose a population P(t) of animals on a small island grows according to a logistic model of the form for some constant .
(a) What is the carrying capacity of the island under this model?
(b) Given that the population is growing and that , is the constant k positive or negative, and why?
(c) Explain why for small values of .
(d) Explain why for values of that are close to the carrying capacity
Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.
Explain how equality is relevant to Euler鈥檚 method.
Sketching disks ,washers and shells : sketch the three disks , washers , shells that result from revolving the rectangles shown in the figure around the given lines
y axis .
For each pair of definite integrals in Exercises 13鈥�18, decide which, if either, is larger, without computing any integrals.
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