Math 252 Test Three
Calculus II name
This easy fifty minute test covers sections 8.8, 10.1,4,5,7 and 11.1,2 of Calculus by James
Stewart 4th ed. Clearly indicate your answers and show your work. All parts of
problems are five points each (unless otherwise stated).
1. Evaluate the following improper integrals.
a)
3
2
1
6x
xe dx
∞−
∫
b)
6
0
1dx
xx
∫
2. For which values of k does the function y = kt
esatisfy the differential equation
y”−3y’−10y = 0.
3. A bacteria culture starts with 2 bacteria and grows at a rate proportional to its size.
After 30 minutes the culture contains 128 bacteria.
a) Find an expression for the number of bacterial after t minutes.
b) What will be the population after 60 minutes?
c) When (after how many minutes) will the population reach 1,000,000.
