MATH 220H, Fall 2016 Quiz 1
Write your name in the top right corner of this sheet.
Show all work clearly and in order. Box your final answers.
Problem 1. Which of the following four matrices are reduced
1 8 0
1 0 0 0 1
1 2 0 0 3
0 0 1
0 1 0 1 0
0 1 0 0 4
Math 141
More Integration Practice
For each of the following integrals decide What method to use. After you ve made your
educated gum go back and try them out.
1) [:084:dz 2) jzzsinhda:
W
3) f t? at 4) [at
2t3+2t+1dm 4237
7)/t(:+1)id 22;
9) [sin
SERIES PRACTICE
Does each series converge or diverge? What test would you use to show
this? Find the sum of the series when easily possible with our current
methods.
P
P
1)
1
1.1
n=1 n
2)
1
2
n=2 n 1
3)
4)
(1)n n
P
n2 + 1
n=1
5)
(1)n n
P
n3 + 1
n=1
6)
Polar Graphs to KNOW
1) Line
2) Circles
o
r
a
r acos
r asin
3) Cardioid
r a acos
r a acos
r a asin
r a asin
r a bcos
Cardioids are a type of Limacon.
b
a
r a bsin
4) Roses
r acosn
r asinn
5) Lemniscate
6) Various Spirals
# of leaves
r2
a2 cos(2 )
r2
a2 si
12.8-12.11 Review
General form of a power series centered at 0:_
General form of a power series centered at a :_
Generally, what test is used to find the radius of convergence and the interval of convergence of a power
series?
How do you determine if the