MAT 127, Lecture 01, Spring 2011
Solutions to Midterm 1
Test the following series for convergence.
1.
n=1
nen .
Answer: Divergent.
Solution: Let us use the Ratio Test: an = nen ,
an+1 = (n + 1)en+1 ,
an+1
n+1
(n + 1)en+1
L = lim
= e lim
= e.
= lim
n
n a
n
MAT 127, MIDTERM 1
PRACTICE PROBLEMS
The midterm covers chapters 8.1 8.6 in the textbook. The actual exam will contain 5
problems (some multipart), so it will be shorter than this practice exam.
1. Determine whether the following sequence converges. If it
MAT 127
Page 1 of 5
Solutions to First Midterm
1. A culture of bacteria grows at a rate proportional to the number of bacteria present in
the culture. At noon on January 24, there were 15 thousand bacteria. At 2 PM, there
were 60 thousand present.
(a) 12
MAT 127, MIDTERM 2
PRACTICE PROBLEMS
The midterm covers chapters 7.1-7.3 and 8.8 in the textbook. The actual exam will contain
5 problems (some multipart), so it will be shorter than this practice exam.
1. Calculate the second degree Taylor polynomial T2
MAT 127, MIDTERM 2
PRACTICE PROBLEMS
The midterm covers chapters 7.1-7.3 and 8.8 in the textbook. The actual exam will contain
5 problems (some multipart), so it will be shorter than this practice exam.
1. Calculate the second degree Taylor polynomial T2
Name:
ID#:
Test # 1
MAT 127 Spring 2005
Directions: There are 5 questions. You have until 10 PM (90 minutes). For credit, you must
show all your work, using the backs of the pages if necessary. You may not use a calculator.
1.
/20
Total Score.
2.
/20
3.
/
MAT 127: Calculus C, Fall 2009
Final Exam Information
Monday, 12/14, 8:15-10:45am
L01,L02: Old Chemistry Bldg 116
L03,L04: Earth&Space (ESS) Bldg 001
General Information
(0) The exam will begin at 8:15AM on the very first day of the exam week; do not miss
MAT 127, CALCULUS C, SPRING 2015
Course Description
This is the final course of the three-semester calculus sequence MAT 125, 126, and 127. We shall
cover differential equations of first and second order, sequences and series, power series, and their
appl
MAT 127: CALCULUS C, FALL 2014
Course Description
We begin by reviewing how to compute derivatives and antiderivatives. Then
we examine first and second order differential equations: what are they;
how can these diffential equations be solved; of what use
Page 1 of 3
Solutions to MAT127 Fall05 Midterm 2
1. The graph below shows a trajectory in the phase plane for a certain predator-prey model. R
denotes the number of rabbits and W denotes the number of wolves. Initially (at time t = 0),
R = 1000 and W = 40
Midterm # 2
MAT 127
Last Name
I.D.#
,
First Name
Lecture#
Question
Points
1
20
2
10
3
20
4
30
5
20
Total:
100
Score
Stop!
Do Not Open This Exam Booklet
Until You Are Told to Do So!
Exam Rules:
No Calculators. No Books. No Notes.
Show all your work, explai
MAT 127 Midterml, Page 2 Oct 6, 2005
Name: M Id: _
1. Find the solution y(x) of the initial value problems
(a) (10 points)
$31533- : Sxelx @ I $3
(b) (10 points}
30's: SJ/(QIXCIX. 3’56”) 2 1
IIUTECJLATE B‘i PNLT3 "
Mr: x dv = €2de MAT 127 Midterm1, Page
MAT 127 Final, Page 2
Name: ._._._._._._._ Id:
Dec 21, 2005
1. (10 points) Find the solution y(x) of the intial value problem
BEE
d3:
EQUA'WOIU (5 SHWBL?’ So
I939;— .-= fame/x
: ygsina:
I
“- :‘CDSX‘FC.
5‘
3:4.”
005x *6.
Since 3(0)” \nr- HF"
aosx
QHELK :
Emma’s
Name:
ID#: _— ,
Test # 1
MAT 127 Spring 2005
Directions: There are 5 questions. You have until 10 PM (90 minutes). For credit, you must
show all your work, using the backs of the pages if necessary. You may not use a calculator.
1. _/20 2. _/20 3.
Nma:
[D#:
Final Exam
MT 12'?“ Spring 21115
Diractiuns: Than: are 3 questions. You have until 1:3(1I FM {150 minutes). For credit. guru
mstﬂhownllyaurwk, mingthebaﬂnnfthepagmifmry. Younlaymtuaeacnluulator.
1. _fm 2. _jm 3. _{m 4. _{10 5. _;15 a. 415
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MATH 127
Page 1 of 5
Solutions to First Midterm
1. A culture of bacteria grows at a rate proportional to the number of bacteria present
in the culture. At noon on January 24, there were 5 thousand bacteria. At 2 PM, there
were 20 thousand present.
(a) 12
Math 127 Homework 2, problem 7.2#20
Name:
February, 2006
ID#:
Lec:
7.2, problem 20: The direction field for a differential equation is shown below. Draw, using
a ruler, the graphs of the Euler approximations for the solution curve that pass through the
or
Name:
ID#:
Test # 2(practice)
MAT 127 Spring 2005
Directions: There are 4 questions. You have 1 hour. For credit, you must show all your work,
using the backs of the pages if necessary. You may not use a calculator.
1.
/25
Total Score.
2.
/25
3.
/25
4.
/2
Name:
ID#:
Test # 2(practice)
MAT 127 Spring 2005
Directions: There are 4 questions. You have 1 hour. For credit, you must show all your work,
using the backs of the pages if necessary. You may not use a calculator.
1.
/25
Total Score.
2.
/25
3.
/25
4.
/2
MAT 127
Midterm I
October 6, 2010
8:30-10:00pm
ID:
Name:
rst name rst
L01
L02
L03
MWF 9:35-10:30am
Section:
TuTh 5:20-6:40pm
TuTh 2:20-3:40pm
(circle yours)
DO NOT OPEN THIS EXAM YET
Instructions
(1) Fill in your name and Stony Brook ID number and circle
MAT 127: Calculus C, Fall 2010
Solutions to Midterm I
Problem 1 (10pts)
Consider the four dierential equations for y = y (x):
(a) y = x(1 + y 2 )
(b) y = y (1 + x2 )
(c) y = ex+y
(d) y = exy .
Each of the four diagrams below shows a solution curve for one
MAT 127
Check one:
_ Lecture
Lecture
#1
#3
MIDTERM
I
MWF 9:35 -10:30
T Th 9:50 - 11:10
Name (printed carefully)
_
Signature
_
ID Number
No calculators
Gorsky
Michelsohn
_
are allowed.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Total
1
All Problems. Test for convergen
MAT 127
Early Exam
September 15, 2010
8:30-10:00pm
DO NOT OPEN THIS EXAM YET
Instructions
Mark your answers CLEARLY on the provided answer sheet
(1) Fill in your name and Stony Brook ID number and circle your lecture number on the
provided answer sheet.
(
MAT 127
Check one:
Lecture # 1
Lecture # 2
FINAL
MWF 9:35 -10:30
T Th 9:50 - 11:10
Gorsky
Michelsohn
Name (printed carefully)
Signature
ID Number
No calculators are allowed.
Do all of your work in this exam booklet, and cross out any work the grader
shoul
MAT 127
May 14, 2012
Final exam.
8:15pm-11:00pm
Name:
ID:
Lecture:
DO NOT OPEN THIS EXAM YET
(1) Fill in your name and Stony Brook ID number.
(2) This exam is closed-book and closed-notes; no calculators, no phones.
(3) Please write legibly to receive cre
MAT 127, Midterm 1
September 27, 2012
Test the following series for convergence.
en
1. 1+e2n .
n=1
2.
3.
ln n
n=1 n .
1
n=2 n ln n .
2
4.
n=1
5.
en
n=1 n2 .
6.
n!(n+1)
n=1 (2n)! .
7.
4n2 +(1)n en
.
n=1
n3 +1
8.
9.
10.
nen .
(1)n
n=1 ln n .
1
n=1 2n+l
MAT 127, Midterm 1
September 27, 2012
Test the following series for convergence.
en
1. 1+e2n .
n=1
Solution: We have
0 < an =
The series bn =
n=1
converges. Therefore
2.
en
1
en
< 2n = n = b n .
2n
1+e
e
e
1
n=1 en is a geometric series with r =
n=1 an co
MAT 127
Midterm 1.
February 22, 2012
8:30pm-10:00pm
Name:
ID:
DO NOT OPEN THIS EXAM YET
(1) Fill in your name and Stony Brook ID number.
(2) This exam is closed-book and closed-notes; no calculators, no phones.
(3) Please write legibly to receive credit.
MAT 127
April 4, 2013
Midterm 2.
8:45pm-10:15pm
Name:
ID:
Lecture:
DO NOT OPEN THIS EXAM YET
(1) Fill in your name and Stony Brook ID number.
(2) This exam is closed-book and closed-notes; no calculators, no phones.
(3) Please write legibly to receive cre
Homework 1
Instructions : There are two parts, PART A and PART B. For PART A,
there are 10 problems, and all of them will be graded. Each problem is worth
10 points. Hence, you must do all of the problems in PART A. The problems
in PART B are harder, and
Homework 4
Problem 1. Find the general solution y = y(x) of the following differential
equations.
dy
1+ x
1.
=
dx
1+ y
dy
= xey
dx
3. (sin x)y 0 = x cot x
2.
dy
xex
4.
= p
dx y 1 + y 2
dy
1
+ 2y = 1 , x > 0.
dx
x
Problem 2. Solve the following initial val
Homework 3
Problem 1. This question is about the The Binomial Series.
1. Read Pag. 612-613 from the book.
2. Using the Binomial series, expand the functions
f (x) = 1 + x
1
f (x) = (1+x)
4
f (x) =
1
1x2
1
that
1x2
= sin1 (x).
3. Use the expansion of
PRACTICE MIDTERM
MAT127
Problem 1. Decide whether the following sequences converge or
diverge. If the sequence is divergent, explain.
n1
1n2 +3n
P
sn = nk=1 k!1
sin n
n! n=1
an =
an = ln(3n + 1) + ln(n 1) ln(7n2 + 3)
an =
xn
n!
x any number
Problem 2.
QUIZ 3
MAT127
SOLUTIONS
1. Decide whether the following series is convergent or divergent.
X
(1)n
n=0
en+1
Solution. This is a geometric series. Notice
n
1
X
(1)n X (1)n X 1
1
e
=
=
=
n+1
n
e
e
e
e
e
1+
n=0
n=0
n=0
1
e
=
1
1+e
Thus, the series is converg