Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Problem Set 11 Questions - Problem Seminar | MATH 289, Assignments of Mathematics

University of Michigan (UM) - Ann ArborMathematics

Material Type: Assignment; Class: Problem Seminar; Subject: Mathematics; University: University of Michigan - Ann Arbor; Term: Fall 2006;

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

koofers-user-av3
koofers-user-av3 ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 289 โ€“ Fall 2006 โ€“ Problem Set 11
Due November 22, 2006
1.(10) Find a number divisible by 2 and 49 which has exactly
a) 22 divisors, b) 23 divisors.
2.(10) Determine a, b so, that (for polynomials)
(xโˆ’2)2divides ax4+bx3+ 2 .
3.(15) For every nโˆˆN, find the largest integer kfor which
2kdivides b(3 + โˆš11)2nโˆ’1c.
4.(20) Does there exist a function f:Rโ†’Rwith the following properties:
(a) fis unbounded at every finite interval (a, b) but it is bounded on any bounded
set of rational numbers?
(b) fis strictly increasing and is continuous at every irrational number but dis-
continuous at every rational number?
(c) fis strictly increasing and is continuous at every rational number but discon-
tinuous at every irrational number?

Partial preview of the text

Download Problem Set 11 Questions - Problem Seminar | MATH 289 and more Assignments Mathematics in PDF only on Docsity!

Math 289 โ€“ Fall 2006 โ€“ Problem Set 11

Due November 22, 2006

1.(10) Find a number divisible by 2 and 49 which has exactly

a) 22 divisors, b) 23 divisors.

2.(10) Determine a, b so, that (for polynomials)

(x โˆ’ 2)^2 divides ax^4 + bx^3 + 2.

3.(15) For every n โˆˆ N, find the largest integer k for which

2 k^ divides b(3 +

11)^2 nโˆ’^1 c.

4.(20) Does there exist a function f : R โ†’ R with the following properties:

(a) f is unbounded at every finite interval (a, b) but it is bounded on any bounded set of rational numbers?

(b) f is strictly increasing and is continuous at every irrational number but dis- continuous at every rational number?

(c) f is strictly increasing and is continuous at every rational number but discon- tinuous at every irrational number?