Name:
Math 2260 Exam #2
March 9, 2012
Instructions: You are welcome to use one sheet of notes, but no other references or tools are allowed
(no textbooks, no calculators, etc.). This is a 50 minute exam; you may start working at 10:10 am
and must stop at 11:00 am. To receive full credit for a correct answer you must demonstrate how you
arrived at that answer. To receive partial credit for an incorrect answer your work must be clearly
explained.
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1. Integrate
Z
x2
x
dx.
− 5x + 4
2
2. Does the improper integral
Z
∞
xe−2x dx
0
converge or diverge? If it converges, find the value of the integral.
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3. Evaluate the definite integral
Z
1
√
0
4
x2
dx.
1 − x2
4. Find an antiderivative for the function
f (x) = e3x cos(x).
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5. A super-fast-growing bacteria reproduces so quickly that the rate of production of new bacteria is
proportional to the square of the number already present. If a sample starts with 100 bacteria, and
after 3 hours there are 200 bacteria, how long after the starting time will it take until there are
(theoretically) an infinite number of bacteria?
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