Math 166
Final Exam 2013/12/17
Name & Section:
Instructor:
Write the solution to each problem. Show steps of calculations, justify
conclusions, and give exact results unless decimal approximations are
requested. No credit is allowed for mere answers with
2014 Fall 166 Final answers
1.
R 2 1
0
2
2 (2 cos 2)
P
2. (a) If
2
2
dt = 2
ak converges, then lim ak = 0.
k=0
k
(b) If 0 ak bk for all k > 0 and
P
P
bk converges then
k=0
(c) Skip this part.
3. 6
4. (a) x
x2 x3
+
2
3
5
12
(c) 6
(b)
6
1 4
2
= 0.015625
4
Calculus II Section N
Spring 2012
Quiz 7 solution
1
lim cos(x) x
x0
The limit evaluation gives us : 1 and this is an indeterminate form
1
now let y = cos(x) x
1
ln(y ) = ln(cos(x) x )
1
x
ln(y ) =
ln(cos(x)
now taking the limit on both sides
1
ln(cos(x)
Calc II Math 166
Name:_
Quiz 1
Volumes using cross-sections, disks, and washers
You may use technology, but show all work.
A. (3 pts) Sketch the region bounded by the line y=3x+4,
and the parabola y=x2, and sketch the solid generated by
revolving this reg