Math 30: Unit 2 Exam
Fall Semester 2006
Instructions. Read each problem carefully and follow all of its instructions. For each of the prob-
lems below, write a clear and concise solution in your blue book. For any short answer questions,
write clearly your answer and any additional explanation that is needed.
1. (5 points) Consider the function f(x)graphed below.
1
x
f(x)
Suppose we have computed the LE FT, RIGHT, MIDP T and TRAP approximations to Z1
0f(x)dx
and get the following four values (each using the same number of subdivisions).
I) 0.36735 II) 0.39896 III) 0.36814 IV) 0.33575
Unfortunately, we forgot which values corresponded to which approximations! Determine
which number corresponds to which approximation and explain how you know this. You
must provide an explanation to receive full-credit.
2. (5 points) Does Z∞
1
2+e−z
zdzconverge? Explain clearly how you know.
3. (5 points) A circular cone has base radius 10 cm and height 5 cm. Use the method of slicing
to find the volume of this cone.
CONTIN UED ON TH E BACK
