Analysis I, section 5 - Midterm (10/22/2013) [100 marks]
Name:
Please justify all your answers, unless otherwise instructed. No calculators allowed.
Duration: 75 minutes.
1. Provide precise denition f
MATH-UA.325.005: Analysis 1.
Homework 1
9/5/13
Solutions to be returned by the beginning of recitation on Friday, 9/13.
1. (3 marks) The positive part of a R is dened by
a+ =
|a| + a
2
and the negativ
MATH-UA.325.005: Analysis 1.
Homework 2
9/12/13
Solutions to be returned by the beginning of recitation on Friday, 9/20.
1. (3 marks) A dyadic rational is a number of the form k/2n for some k, n Z. Pr
MATH-UA.325.005: Analysis 1.
Homework 6
10/12/13
Solutions to be returned by the beginning of recitation on Friday, 10/18.
1. Decide which of the following statements are true and which are false. Pro
MATH-UA.325.005: Analysis 1.
Homework 9
11/07/13
Solutions to be returned by the beginning of recitation on Friday, 11/15.
1. Assume that (ex ) = ex . Decide which of the following statements are true
MATH-UA.325.005: Analysis 1.
Homework 7
10/31/13
Solutions to be returned by the beginning of recitation on Friday, 11/8.
1. Suppose that I is an open interval containing a and f, g : I R are in C (I)
MATH-UA.325.005: Analysis 1.
Homework 7
10/25/13
Solutions to be returned by the beginning of recitation on Friday, 11/1.
1. (a)
Let I be a bounded interval. Prove that if f : I R is uniformly
continu
MATH-UA.325.005: Analysis 1.
Homework 4
9/26/13
Solutions to be returned by the beginning of recitation on Friday, 10/4.
1. Find the limit (if it exists) of the following sequences.
(1 mark) xn = 2n/
Analysis I, section 5 - Final Exam (12/17/2013) [100 marks]
Name:
Please justify all your answers, unless otherwise instructed. No calculators allowed.
Duration: 100 minutes.
1. Provide precise deniti
Analysis Spring 16 - Complement to the Infinite series
chapter
Lise-Marie Imbert-Gerard
March 23, 2016
What we call comparison test for series is any test to conclude
P that a series
converges by usin
Topics to Review for Final Exam
From the Past:
1) Understand how to solve the basic labor supply model (e.g. like the
problem on the First Midterm), possibly with a different utility function (e.g.
Econ-UA 353 HW #3 Solution
Question 1.
(1) The employees expected utility from choosing eH is 0.8 2500 + 0.2 0
16 = 24, while her expected utility from choosing eL is 0.4 2500+0.6 00 =
20. Choosing e
Lecture 22 Announcements
Today
- Finish Human Capital (just paper)
- Start Inequality
(Chapter 15)
Reminder Stata Tutorial tomorrow night 7:00-9:00 PM.
Room TBD, will email you as soon as I know
Hum
Lecture 19 Announcements
Today: Part 2 of Human Capital (Chapter 9)
Goals from Last Lecture
1) Definition of Human Capital (Beckers Quote), parallels to Physical
Capital
2) Know basic costs and ben
Lecture 16 Announcements
Today: Talk Contracts / Incentives (Chapter 11)
Todays lecture will not be on Midterm 2, will be on Final
Exam
Reminder: The second midterm will take place on
Wednesday, Ap
Lecture 23 Announcements
Today
- Continue Inequality
(Chapter 15)
Will Collect Response Papers for Autor Levy Murnane at
the end of class.
Goals
1) Recall three motivating facts from the Data in Pi
Lecture 17 Announcements
Today: Talk Contracts / Incentives (Chapter 11)
Reminder: The second midterm will take place on
Wednesday, April 6. Will have a review session
TONIGHT, 7:30-9:30, in Silver
Final exam reminder:
December 21 (Wednesday), 4:00PM - 5:15PM
Same room as lectures
Econ-UA 353 Practice Questions III
Question 1.
Suppose an industry has ten firms. The market shares of each firm are
Lecture 20 Announcements
Today: Part 3 of Human Capital (Chapter 9)
Six classes left:
Today Post-Schooling Investments in Human Capital
Wednesday 4/20 Pre-Schooling Investments in Human Capital
M
Lecture 13 Announcements
Material on the Radar:
Chapter 5: Frictions in the Labor Market
- Monopsony, Job Search
Chapter 13: Unions and the Labor Market
Chapter 11: Contracts / Incentives in Firm
MATH-UA.325.005: Analysis 1.
Homework 6
Solutions
1. Decide which of the following statements are true and which are false. Prove the
true ones and provide counterexamples for the false ones.
(1 mark
MATH-UA.325.005: Analysis 1.
Homework 10
11/14/13
Solutions to be returned by the beginning of recitation on Friday, 11/22. You can use
only denitions and those theorems that we proved on class.
1. (2
Analysis I, section 6 - Solutions to Quiz 1 (10/04/2013) [10 points]
1. [2 points] Recall the Field Axioms (closure, associative and commutative properties for sum and product, distributive law, addit
Analysis I, section 6 - Solutions to Quiz 4 (12/06/2013) [10 marks]
1. Let f (x) = 2x3 .
(a) [2 marks] Using the Fundamental Theorem of Calculus, nd
2
0
f (x)dx.
Solution:
According to the Fundamental
Analysis I, section 6 - Solutions to Quiz 3 (11/15/2013) [10 marks]
1. Let f : R R be a function.
(a) [2 marks] State the denition of f (a), the derivative of f at a R.
Solution:
f (a) = lim
ha
f (a +
MATH-UA.325.005: Analysis 1.
Homework 5
10/03/13
Solutions to be returned by the beginning of recitation on Friday, 10/11.
1. (3 marks) Let cfw_xn be a real sequence and r a real number. Prove that l
Melody Duan
Real Analysis HW2 due 9/29/2017
Sec 1.3 Ex 5, 11, 12, 13, 20
a) neither open or closed.
S 0=(1,2 ) (3, )
Sc
b) open.
S 0=( ,1 ) (2, )
Sc
S
( 0) =( ,1 ] [2,3]
c
c) closed.
0
S =(3,2 ) (7,8)
2.2.9. a) Let E = cfw_k Z : k 0 and k 10n+1 y . Since 10n+1 y < 10, E cfw_0, 1, . . . , 9. Hence w := sup E
E . It follows that w 10n+1 y , i.e., w/10n+1 y . On the other hand, since w + 1 is not the
HOMEWORK 2 SOLUTIONS FOR V63.0325-001: ANALYSIS 1 - SPRING 2011
DMYTRO KARABASH
1. 1.6.7.
(a) We can write q =
(1)
m
k,
m, k Z, k = 0. Then we want to nd when equation for which
x = nq
is a solutions.