Ryerson University - MTH 525 Assignment 6, part 1
Date due: Friday, Nov 13h
Problem 1 Let
f (x) =
x(x 1)(x 3)
From the definition of limits, show that limx2 f (x) = 5/2.
Problem 2 Suppose that f and g are functions such that
lim f (x) = ` and
Ryerson University - MTH 525 Assignment 7
Date due: Friday Nov 27, 2015
Problem 1 Suppose that f is continuous on [0, 1] and f (0) < 0, f (1) > 1.
Show that there is some x (0, 1) such that f (x) = x2015 .
Problem 2 (a) Let f be real-valued and continuo
Ryerson University - MTH 525 Assignment 3
Date due: Friday, Oct 9
Problem 1 Suppose that cfw_ak , cfw_bk are sequences such that cfw_ak converges.
Assume also that
lim |ak bk | = `
for some ` R.
(i) If ` = 0, must it follow that cfw_bk also converg
Ryerson University - MTH 525 Assignment 4
Date due: Friday, Oct 23
Problem 1 For each of the following statements, either prove that it is true
or give a counter-example.
(i) If a sequence is not bounded, then it must have a subsequence diverging
Ryerson University - MTH 525 Assignment 5
Date due: Friday, Oct 30th
Let S R. Let O be a collection of subsets of R. So, each element of O
is itself a subset of R.
(a) We say that O is a cover for S if
That is, the union of all sets in O conta
MTH 525 - Assignment 5
November 19, 2015
Let (xk ) be a sequence that converges to `. Let E := cfw_xk : k N cfw_`.
Let O be an arbitrary open cover for E.
Because ` E, there is some open set O` O that contains `. So there exists ` > 0
Ryerson University - MTH 525 midterm cheat sheet #1
Let (xk ) be a sequence. Let E R. Then
(a) (xk ) is increasing if there is a positive integer N such that xk xk+1 for
all k N .
(b) (xk ) is decreasing if (xk ) is increasing.
(c) (xk ) is monotone if it
Ryerson University - MTH 525 Assignment 2. Due next Friday, Sept 25,
2015 in class.
7k 4 + 5k 3 + 11k 2 k + 11
3k 4 + 2k 3 7k + 5
for all k N.
Find, if possible, a constant A and a positive integer M so that
for all k
Ryerson University - MTH 525, Fall 2015- Assignment 1
Date due: Friday, Sept 18, at the start of class
1. Modify the argument given in class to show that for any
positive a,there is a unique positive x such that x2 = a. We denote
this x by a.