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)
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