Homework 8 Math CS 120, Winter 2009
Due on Thursday, March 12th, 2009
1. Investigate the convergence of
an where
(a)
an =
(b)
n+1
n+1
n
.
n+1 n
.
n+1
an =
2. Let
an and
bn converge, with bn > 0 for al
CCS Math 120: Calculus on Manifolds
Simon RubinsteinSalzedo
Spring 2004
0.1
Introduction
These notes are based on a course on calculus on manifolds I took from Professor
Martin Scharlemann in the Spri
Daisy He
August 29th, 2013
Do not judge people with their appearance. People have been learning this from their
parents, schools, friends, and life experences thoughout their life, but only one out of
Identifying Rhetorical Strategies: Logos, Pathos, and Ethos
Rhetoric: The art of using language persuasively and effectively
Logos = Logic
Pathos = Emotion
The use of logic, rationality, and critical
Review Material
For ACCTG 10
Final Exam
Accounting is called the language of business; therefore it is essential that you are to match
the following terms with their definitions on the exam.
Account n
Homework 8 Math CS 120, Winter 2009
Due on Thursday, March 12th, 2009
1. Investigate the convergence of
an where
(a)
an =
(b)
n+1
n+1
n
.
n+1 n
.
n+1
an =
2. Let
an and
bn converge, with bn > 0 for al
Homework 7 Math CS 120, Winter 2009
Due on Thursday, February 26th, 2009
1. Let f : [a, b] R be a continuous function, dierentiable in (a, b).
Prove that if f (x) = 0 for all x (a, b), then f is a con
Homework 6 Math CS 120, Winter 2009
Due on Thursday, February 19th, 2009
1. Given A Rn , and z Rn , prove that the following statements are
equivalent:
(a) z A (the closure of A, also denoted by cl(A)
Homework 1 Math CS 120, Winter 2009
Due on Thursday, January 15th, 2009
1. Prove that the function
x
: Rn R dened by
= max |xi |
1in
is a norm.
2. Prove that the function
: Rn R dened by
1
n
x
|xi |
=
Homework 2 Math CS 120, Winter 2009
Due on Thursday, January 22nd, 2009
1. Prove that a convergent sequence cannot converge to two dierent
limits.
2. Consider the sequence of real numbers
an = n + 1 n
Homework 3 Math CS 120, Winter 2009
Due on Thursday, January 29th, 2009
1. Consider a sequence of real numbers cfw_xn nN R. Prove that if there
exists a subsequence of cfw_xn nN that converges to b R,
Homework 3 Math CS 120, Winter 2009
Due on Thursday, January 29th, 2009
1. Consider a sequence of real numbers cfw_xn nN R. Prove that if there
exists a subsequence of cfw_xn nN that converges to b R,
Homework 4 Math CS 120, Winter 2009
Due on Thursday, February 5th, 2009
1. Consider the Fibonacci sequence a1 = a2 = 1, and
an+1 = an + an1 , n 2.
Prove that
an+1
n an
lim
exists, and nd the limit.
2.
Homework 5 Math CS 120, Winter 2009
Due on Thursday, February 12th, 2009
1. Consider Rn , and the norms
p,
for 1 p < .
(a) Find constants cp > 0, dp > 0 such that
cp x
p
x
dp x p , x Rn .
(b) For any