Homework Quiz 6
MTH 3315
Name: 50 U'Ho/u
Answer all questions. You may use your homework. You may not use a calculator.
l. (4 points) [Ch. 6, #22] Let (b be an automorphism of group G. Prove the set H = {:5 e
G | ¢(:r) = :17} is a subgroup of G.
IA o
MTH 2401 - Calculus II
Your Name
Exam 2
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Spring 2011
50
Score
This exam is closed book. A single handwritten 35 note card is allowed for reference.
Calculators are not allowed.
In order
Calculus II
Maple Lab 5
Taylor Polynomials
Todays lab is an overview of Talyor polynomials. The general motivation to use them is that general
functions are hard to work with, but polynomials are easy (relatively speaking). If we could write any
general f
Calculus II
Maple Lab 6
Innite Series and the Harmonic Series
Maple can be used to test the convergence of a series with little diculty. By now you have seen
basically all the tools you need to do this. Lets say you want to know whether or not
n=1
1
n2
co
Calculus II
Maple Lab 8
Power Series
Today we will extend some of what we have done with Taylor polynomials to power series and intervals
of convergence.
Recall that in class we derived the following power series for the inverse tangent:
tan1 x =
(1)n
n=0
Calculus II
Maple Lab 9
Parametric Equations
This lab will be a preview of the material we will be covering for the rest of chapter 10, called parametric
equations. These are graphs in the x y plane that are dened through functions of a parameter, general
MTH 2401 - Calculus II
1
(10 points)
(a)
Exam 1 Solutions
Spring 2011
Evaluate the following integrals:
x2 4 x2 dx
Solution:
When you draw a triangle, you get that
x = 2 cos
4 x2 = 2 sin
dx = 2 sin d
When you plug this into the integral, you get:
16 cos
MTH 2402 - Calculus II
Your Name
Final Exam
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Total
Spring 2011
70
Score
This exam is closed book. You can use one handwritten 8.511 page of notes for reference.
Calculators are not al
MTH 2401 - Calculus II
Your Name
Final Exam
Your Signature
Problem
Total Points
1
6
2
6
3
8
4
6
5
6
6
6
7
6
8
6
Total
Spring 2009
50
Score
This exam is closed book.
Calculators are not allowed.
In order to receive credit, you must show your work. You m
Calculus II
Maple Lab 10
Polar Equations
Tomorrow in class we will start on polar coordinates, so lab today will be a small preview of this strange
way of graphing. We start with a simple looking equation.
r() = .
In polar coordinates, this is describing
MTH 2402 - Calculus II
Your Name
Final Exam
Your Signature
Problem
Total Points
1
6
2
6
3
8
4
6
5
6
6
6
7
6
8
6
Total
Spring 2010
50
Score
This exam is closed book.
Calculators are not allowed.
In order to receive credit, you must show your work. You m
MTH 2401 - Calculus II
Your Name
Exam 2
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
15
5
5
Total
Spring 2010
50
Score
This exam is closed book. A single handwritten 35 note card is allowed for reference.
Calculators are not allowed.
In order t
MTH 2401 - Calculus II
Your Name
Exam 2
Your Signature
Problem
Total Points
1
10
2
15
3
6
4
12
5
7
Total
Spring 2009
50
Score
This exam is closed book.
Calculators are not allowed.
In order to receive credit, you must show your work. You must also just
MTH 2401 - Calculus II
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
10
3
10
4
10
5
10
Total
Spring 2011
50
Score
This exam is closed book. A single handwritten 35 note card is allowed for reference.
Calculators are not allowed.
In order
MTH 2401 - Calculus II
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
8
3
8
4
8
5
8
6
8
Total
Spring 2010
50
Score
This exam is closed book. A single handwritten 35 note card is allowed for reference.
Calculators are not allowed.
In order
MTH 2401 - Calculus II
Your Name
Exam 1
Your Signature
Problem
Total Points
1
10
2
8
3
8
4
8
5
8
6
8
Total
Spring 2009
50
Score
This exam is closed book.
Calculators are not allowed.
In order to receive credit, you must show your work. You must also ju