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Chapter 5: Problem 37
Evaluate the definite integral. \(\int_{0}^{4}\left(x^{1 / 2}+x^{1 / 4}\right) d x\)
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Find the change in cost \(C\), revenue \(R,\) or profit \(P,\) for the given marginal. In each case, assume that the number of units \(x\) increases by 3 from the specified value of \(x .\) Marginal \(\quad\) Number of Units, \(x\) \(\frac{d C}{d x}=2.25 \quad x=100\)
The rate of change of mortgage debt outstanding for one- to four-family homes in the United States from 1998 through 2005 can be modeled by \(\frac{d M}{d t}=5.142 t^{2}-283,426.2 e^{-t}\) where \(M\) is the mortgage debt outstanding (in billions of dollars) and \(t\) is the year, with \(t=8\) corresponding to \(1998 .\) In \(1998,\) the mortgage debt outstanding in the United States was \(\$ 4259\) billion. (a) Write a model for the debt as a function of \(t .\) (b) What was the average mortgage debt outstanding for 1998 through \(2005 ?\)
Use a graphing utility to graph the function over the interval. Find the average value of the function over the interval. Then find all -values in the interval for which the function is equal to its average value. Function \(\quad\) Interval \(f(x)=\frac{6 x}{x^{2}+1} \quad[0,7]\)
State whether the function is even, odd, or neither. \(f(t)=5 t^{4}+1\)
Find the amount of an annuity with income function \(c(t),\) interest rate \(r,\) and term \(T .\) \(c(t)=\$ 1500, \quad r=2 \%, \quad T=10\) years
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