2- (a)
.11
a
:72. ., "
«Ham 4 u
0:
\
., _
VJ .. 2m
_.\\
_\\
1/1:\\l:/i _
D.
{ ,
. . a.
as
f. N f
Q3!
J...
R
[ :
.43 ii?
xx. .
J <
W
i
f; f,
r
1 w .
U}: IIIIJWRPI'IIIPIJ
/ //:J..fl.f.l.lun
at
r1. a r
(\N
l\\\\\
V
Homework 1 Sample Solutions
provided by Alex Grounds
Extra Exercise 1. Show that for a, b (0, ),
ln a ln b = ln
a
b
Solution. Lets dene z = ln a ln b. Exponentiating, we get ez = eln aln b . Using the facts
that ea+b = ea eb and ea = e1 , we obtain
a
z
e
HOMEWORK 1 EXTRA EXERCISES
The point of these exercises is to review some facts that we came across in class. It seems
that most of you believe these facts and are willing to use them, but are not sure why they
are true.
The goal is
(1) to convince yourse
Solution Sample to HW3
Monday, February 16, 2015
4:57 PM
provided by Junyan
New Section 4 Page 1
this problem will
not be graded
In this last question it is not entirely clear if the order of the groups matter or not.
If it mattered, then the answer would
Homework 2 Sample Solutions
provided by Kenneth Co
Extra Exercise 1. (a) Show that the following decomposition cannot hold
x3 + 10x2 + 3x + 36
Bx + C
A
+ 2
=
2 + 4)2
(x 1)(x
x 1 (x + 4)2
for constants A, B, and C.
(b) Show that the following decomposition
Homework 5 Sample Solutions
Prepared by: Diego A. Espinoza
March 13, 2015
4. Roll a fair die twice. Let X be the random variable that gives the maximum of the
two numbers. Find the probability mass function describing the distribution of X.
Solution: Obse
Homework 7 Sample Solutions
Exercise 8.1 #14. Solve
dx
dt
= 1 3x, where x(1) = 2.
Solution. We separate variables and integrate to obtain
dx
=
1 3x
dt = t + C
To compute the lefthand integral, we use u substitution, with u = 1 3x, du = 3 dx:
dx
1
=
1 3x
3
NOTE ON LOGISTICS EQUATION
If you nd any errors or typos in this note, please alert me.
The logistics equation is
dy
= ky(M y),
dt
where k and M are positive constants that we interpret in the following way. This equation is used to model things like spre
MATH 109 SYLLABUS
Instructor: Maxim Arap
Course: MATH 109
E-mail: [email protected]
Oce: 311 Krieger Hall
Course description
Sections of the book: 7.1-7.4, 9.1-9.5, 10.1-10.4, 7.8, 11.1-11.11
Textbook
Single Variable Calculus: Early Transcendentals, 7th
Exam 1 Practice
February 27, 2015
Exam 1 Practice
February 27, 2015
1 / 22
Exercise 1
For any two events A and B,
P(A|B) = P(A)
.
(a) TRUE
(b) FALSE
Exam 1 Practice
February 27, 2015
2 / 22
Exercise 1
For any two events A and B,
P(A|B) = P(A)
.
(a) TRUE
(
Exam 2 Practice
April 11, 2015
Exam 2 Practice
April 11, 2015
1 / 41
Exercise 1
For a random variable X , the expected value of the random variable 3X is
E (3X ) = 3E (X ).
(a) TRUE
(b) FALSE
Exam 2 Practice
April 11, 2015
2 / 41
Exercise 1
For a random v
1. Determine Whether the sequence converges or diverges. If it converges, nd the limit.
(a) an : sinin) 2. (a) Compute the integral:
r5§§|liii§
K 3. Find the eXact length of the polar curve 7" = 200s(6) for 0 S 6 S 7r/2.
'1
(L9 9 A
PRACTICE EXAM
1. Midterm 1 Material
1.1.
Dierential Equation.
1.1.1.
#1.
Solve the following dierential equation when
x=
3
5
and
y = 1.
dy
= 4y 4 x
dx
1.1.2.
#2.
Find the equilibrium points for the dierential equation.
dy
= (y + 1)(y 1)(y 2)
dx
1.1.3.
1.2
problems
1 6(34)
7 13(34) 14 19(34)
total(102)
scores
Final Exam, December 10, Calculus II (107), Fall, 2014, W. Stephen Wilson
I agree to complete this exam without unauthorized assistance from any person, materials or device.
Name (signature):
Date:
Nam
Math 107: Calculus II, Spring 2015: Midterm Exam II
Monday, April 13 2015
Give your name, TA and section number:
Name:
TA:
Section number:
1. There are 5 questions for a total of 100 points. The value of each part of each question is stated.
2. Do not ope
Math 107, Spring 2015: Midterm II Study Guide
The second midterm exam will take place on Monday April 13. There will be two dierent
rooms for the exam and these will be the same as for the rst midterm. It will
be 50 minutes long, starting promptly at 10am
Department of Mathematics at Johns Hopkins University
AS.110.109 Calculus II (Eng) Instructor: Maxim Arap Spring 2013
Midterm Exam 2
To get full credit you must Show all of your work. You have 50 minutes to
complete the exam.
Academic Honesty Certica
Math 107: Calculus II, Spring 2014: Midterm Exam I
Monday, March 2 2015
SOLUTIONS
i
1. (a) (10 points) Write the correct form of the partial fraction decomposition of the following rational
function. Do not evaluate the undetermined coecients.
x2 (x2
x3 +
Final Practice
May 1, 2015
Final Practice
May 1, 2015
1 / 30
Exercise 1
The functions x(t) = e 2t and y (t) = e 2t are a solution to the system
of dierential equations
dx
= 2x + 4y
dt
dy
= x 3y .
dt
(a) TRUE
(b) FALSE
Final Practice
May 1, 2015
2 / 30
Exe
Math 107, Spring 2015: Midterm I Study Guide
The rst midterm exam will take place on Monday 2 March. There will be two dierent
rooms for the exam and these will be announced soon. It will be 50 minutes long,
starting promptly at 10:00am, and 11am, respect