MAT2125 Elementary real analysis (Winter 2016)
Homework assignment 2
Solutions
1. Prove without using the limit theorems for sequences that
lim
n
n+2
1
= .
2n 3
2
Solution. Denote our sequence by fn =
MAT 2125 Mid-Term Examination 2015 Solutions
1. a) If cfw_an n
1
is a real sequence, and a 2 R, give the denition of
lim an = a.
n!1
Solution:
8" > 0 9N 2 N such that k
or
8" > 0 9N 2 N such that 8k
[
MAT2125 Elementary real analysis (Winter 2016)
Homework assignment 3
Solutions
1. Determine whether the series
it absolutely converges.
n
n=1 (1)
P
sin n converges and whether
P
Solution. A necessary
MAT2125 Elementary real analysis (Winter 2016)
Homework assignment 4
Solutions
1. Prove (by using the definition) uniform continuity of the function
f (x) = 2x 3 on the real line R.
Solution. Since |f
MAT2125 Elementary real analysis (Winter 2016)
Homework assignment 1
Solutions
1. Prove by induction that the sum of the first n odd integers is n2 .
Solution. Put
Sn =
n
X
k=1
(2k 1) ,
so that one ha
University of Ottawa
MAT 2324 Midterm Exam
Feb 26, 2015. Duration: 80 Minutes. Instructor: Robert Smith?
Family Name:
First Name:
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ADM 2350A
October 22, 2014
Quiz #5 Examination
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ADM 2350A
September 17, 2014
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September 24, 2014
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October 1, 2014
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October 31, 2014
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November 7, 2014
Quiz #7 Examination
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November 21, 2014
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MAT 2324
2384-Practice Problems on Homogeneous Euler-Cauchy Equations
For each of the following ODEs, Find the General Solution. If an initial condition is
given, nd also the corresponding particular
MAT 2324
2384-Practice Problems on First-order Separable- Homogeneous
ODEs
1. Find the general solution of each of the following ODEs.
(a) y 0 = 2 sec(2y)
(b) yy 0 + 25x = 0
(c) y 0 sin(x) = y cos(x)
MAT 2324
2384-Practice Problems on Linear Second Order ODEs with
constant coe cients
For each of the following ODEs, Find the General Solution. If an initial condition is
given, nd also the correspond
Problems for Mat2125
1. If a and " are real numbers, prove that
cfw_x | |x
a| < " = cfw_x | a
" < x < a + ",
i.e. that they are equal, as sets!
The set cfw_x | a " < x < a + " is a called an open inte
ADM 2350A
October 8, 2014
Quiz #4 Examination
Version #1 Solutions
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Student ID #: _
Statement of Academic Integrity
The Telfer School of Management does not condone academic fraud, an act by a
A GA> " w'iMAf BTWQ PNGC/Pe/g/a}
" A w Covvziii iagct \(rw Awr
so?
1. Prove the following for subsets of R":
a) An arbitrary union of open sets is open.
b) An arbitrary intersection of
MAT2324 Assignment #2
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MAT2324 Assignment #1
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MAT 2324: Ordinary Differential Equations and the Laplace Transform
Professor:
Dr. Robert Smith? (the question mark is part of my name)
Location:
KED 205G Phone: 613 562 5800 x3864
Lectures:
Tuesdays
MAT 2125 Winter 2017
Assignment 2
Professor: Alistair Savage
Due date/time: February 2, 2017, 3pm
Assignments should be placed in the box for this course found in the lobby of the Department of Mathem
MAT 2125 Winter 2017
Assignment 4
Professor: Alistair Savage
Due date/time: March 16, 2017, 3pm
Assignments should be placed in the box for this course found in the lobby of the Department of Mathemat
MAT 2125 Winter 2017
Assignment 5
Professor: Alistair Savage
Due date/time: March 30, 2017, 3pm
Assignments should be placed in the box for this course found in the lobby of the Department of Mathemat
MAT 2125 Winter 2017
Quiz 2
Professor: Alistair Savage
February 8, 2017
Question (4 pts). Is the series
convergent? Is it absolutely convergent?
X
(1)n1
2n + 3
n=1
MAT 2125 Winter 2017
Assignment 3
Professor: Alistair Savage
Due date/time: February 16, 2017, 3pm
Assignments should be placed in the box for this course found in the lobby of the Department of Mathe