Review #1 Math 3A
The following questions do not cover all the topics covered in sections 1.1 1.6 and 2.1. There may be
questions on the test that are not represented here.
1.
Use the graph to find the following limits
a. lim f x
x 1
b. lim f x
x 2
c.
l
Math 3A
Review #1 Solutions
1.
a. 1
e. I
b.
f. 2
c. 1
g. 3
d. DNE
2.
a. 10
b.
c. 1
5
7
3.
a. 3
f.
b. 16
c.
7
10
12
7
g. 1
h. 1
d. DNE
e.
3
2
4.
a.
e. 10
b. 7
f.
c.
g. 1
d. 0
5.
a.
b.
4
5
e. DNE
f.
c. 1
d. 0
1
1 cos x
1 cos x 1 cos x
lim
x 0
x 0
SADDLEBACK COMMUNITY COLLEGE
Political Science 1 Introduction to American Government (Internet)
Summer 2015: Internet Format (June 15th July 24th) Ticket# 14585
Instructor: Michael McKinney
Email: mmckinney@saddleback.edu
Class Website: socccd.blackboard.
Political Science 1 American Government
Final Exam
Michael McKinney  Summer 2015
After careful consideration and review, answer one of the following four options thoroughly and completely (take
care, there are multiple parts). For your answer, you are ex
Jonathon Church
Segment 16 US  Foreign Policy


Foreign Policy is used to influence behavior toward other central governments
o Both strategic and Tactical techniques are used to influence various issues
o The use of political economic and military all
Math 3b
Solutions: Exam 3
Fall 2015
1. (a) The following statements refer to a sequence cfw_ ak
k=2 . Fill in the blanks. Note
that you may need more than one word or symbol for each blank.
(a) The sequence is eventually decreasing if ak+1 ak is eventual
Math 3b
Exam 1
Spring 2016
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Simplify to the extent we have in class. If you have questions about whether you
need to simplify
Math 3b
Exam 3
Spring 2016
1. Determine whether the following series converges or diverges.
cos2 k
5k + k
k =1
Initial thoughts:
cos2 k will always be positive (cos2 k wont be 0 since cos k 6= 0 for any integer value of k.) We also know that cos2 k < 1
Math 3b
Solutions: Exam 1
1. (12 points) Evaluate.
Z ln 2
0
Spring 2016
cosh x 4 sinh x + 1 dx
Let u = 4 sinh x + 1
du = 4 cosh x
u(0) = 4 sinh
0+1 = 1
0+1 =
u(ln 2) = 4
Z ln 2
0
eln 2 e ln 2
2
+ 1 = 2 2 12 + 1 = 2
cosh x 4 sinh x + 1 dx
=
cfw_z
3
2
+1
Math 3b
Solutions: Exam 1
1. Evaluate.
Z ln 3
sinh3 x
0
=
=
=
=
=
u(ln 3) =
u
u0
du
u (0)
cosh x
dx
cosh x
sinh x
sinh x du
cosh 0
1
cosh(ln 3)
eln 3 + e ln 3
2
1
3+ 3
=
2
=
=
10
3
2
5
=
3
Page 1 of 8
Fall 2015
Math 3b
Solutions: Exam 1
Z ln 3
sinh3 x
0
c
Math 3b
Solutions: Exam 2
1. Evaluate.
Z
1
x 1 x2
Fall 2015
dx
Well try a trig sub for this; if you can see that we want to use a sine substitution,
great. If youre not sure, to figure it out, not that the quantity 1 x2 is under the
radical. As such, it
Math 3b
Solutions: Exam 2
1. Evaluate.
Z
Spring 2016
tanh11 xsech4 x dx
Recall:
cosh2 x sinh2 x = 1
cosh2 x
cosh2 x
sinh2 x
1
=
cosh2 x
cosh2 x
1 tanh2 x = sech2 x
Z
tanh11 xsech4 x dx
Z
tanh11 xsech2 xsech2 x dx
Z
tanh11 x 1 tanh2 x sech2 x dx
Z
u11 1 u2
Math 3b
Exam 2
Spring 2016
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Simplify to the extent we have in class. If you have questions about whether you
need to simplify
Math 3b
Exam 1
Fall 2015
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Simplify to the extent we have in class. If you have questions about whether you
need to simplify fu
Math 3b
Exam 2
Fall 2015
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Simplify to the extent we have in class. If you have questions about whether you
need to simplify fu
Math 3b
Final Exam
Fall 2015
Directions:
Show all work and justify all answers. If you have questions about whether you
need to show more work, you may ask.
Simplify to the extent we have in class. If you have questions about whether you
need to simplif
Math 3b
Exam 3
Fall 2015
Directions: Show all work and justify all answers. Simplify to the extent we have in
class; if youre not sure whether an answer needs further justification or further simplification, ASK!
When testing for convergence, be sure you
Math 3b
Exam 3
Spring 2016
Directions: Show all work and justify all answers. Simplify to the extent we have in
class; if youre not sure whether an answer needs further justification or further simplification, ASK!
When testing for convergence, be sure y
Time
Mon
1
2 Selected Topics in Japanese Grammar
3 Reading Short Novels
4 International Organization
5
6
Tue
Enjoy Life, Culture & Seasonal Events in Japan
Lets Enjoy Talking
International Organizations
Wed
Focusing on Japanese pronunciation
International
Women in Art throughout the Ages
In my project, my task is to research famous paintings of women that were created in different time periods and eras. The art will be collected and all of the women will be measured out so that all of their golden ratios c
Criterion E: Validity I used a variety of mathematical processes to determine the golden ratios for a variety of different types of art. In finding the Golden Ratio I was able to see the changes in how artists depicted the female body throughout each era.
Criterion A: Introduction
Women in Art throughout the Ages
For my IB project I am going to look at women in art throughout the years. I will pick five famous pictures containing women from all different eras in art. With these pictures I will calculate th
Criterion C: Mathematical Processes There are three ratios I chose to find out if the golden ratio was present for each era in art. Golden Ratio Factions: a b 1. Top of head Width of head 2. Tip of nose to chin Lips to chin 3. Length of Lips Width of Nose