# Math 152 Quiz 9

Find the values of p for which the following integrals converge. a) dx x lnx ( )p1 2 b) dx x lnx ( )p2 8
2. (3 points) Determine whether dx ex +e-x- 8 8 converges or diverges. If it converges, find what it converges to. 3. Consider lnxdx 1 5 . Use Es = K(b-a)5 180n4 . a) (3 points ) Give the maximun error bound for using Simpson s Rule to evaluate this integral for n = 6. b) (2 points) How large must n be so that the Simpson s Rule estimate is accurate within 0.001 4. (3 points) Use Euler s Method with step size 0.5 to estimate y(2), where y(x) is the solution to the inial value problem y’=x+xy y(0) = 1.
5. (3 points) A population grows at a rate that is proportional to its population. In 2008 (t = 0) , there were 20,000 people present, In 2014, there were 25,000 people present. Write an initial value problem for this situation, solve it, and estimate the population in 2015.

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