Midterm 2, Math 30, Fall 2008, 11/10/08
Instructions: Write your name and section number. Draw grading table on the cover.
Read each problem carefully and follow all of its instructions. For each of the problems
below, write a clear and concise solution in your blue book. Solutions must be simplified
as much as possible, no full credit for partially completed problems. Blue books with
torn or missing pages will not be accepted !
1. Use the Midpoint rule to find the approximation to ∫+
5
11x
dx with n = 4. You can
leave your answer in terms of the numerical sum. (Exact solution will not get you
full credit!). (10 pts)
2. Trout population in the lake is modeled by the equation.
)3000)(2000(
2PPP
dt
dP −−=
a) Find and identify by type equilibrium points. (4 pts)
b) Plot the fish population over time if the starting population is 2500 (3 pts)
c) Plot the fish population over time if the starting population is 3500 (3 pts)
(Note: In your drawing clearly label points on the axis and explain what
happens to population after a long time)
3. A probability density function is given by 3
)1(
)( +
=x
A
xf for 0≥x and
0)( =xf for x < 0.
a. Solve for A. (5 pts)
b. Find the median (5 pts)
4. A medical laser is cutting a tissue along the arc 2/3
3
2xy = from x = 0 to x = 3 cm.
If the laser spot is moving at 0.1 cm/sec, calculate the time it takes to complete the
cut. (10 pts)
5. For what values of r does the function y = erx satisfy the equation
2y’’ + y’- y=0 (10 pts)
Extra Credit (5 pts)
In problem 3 find the average.