The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
(MATH101)[2001](f)midterm1~4660^_97137.pdf downloaded by whchowad from http:/petergao.net/ustpastpaper/down.php?course=MATH101&id=0 at 20150921 09:40:49. Academic use within HKUST only.
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The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
(MATH2033)[2014](s)midterm~=vnz55et^_10738.pdf downloaded by whchowad from http:/petergao.net/ustpastpaper/down.php?course=MATH2033&id=1 at 20160306 07:55:41. Academic use within HKUST only.
Math 2033 (Mathematical Analysis)
Spring 2014
Midterm
Directio
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 20082009
Homework # 4 Due Friday, March 20, 2009 at 3pm
Be sure to write your name (as shown on your student ID card) and your tutorial
session number on the homework! Show work. Answers are worth very litt
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 201 (Introduction to Analysis)
Spring 20022003
Lectures 1,2,3
Time Limit: 120 Minutes
Final Examination
Remarks. You must show work to receive credits. Answers alone are worth very little. The
symbols
and
denote the set of all real numbers and the s
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
(MATH2033)[2015](s)final~hrtin^_93328.pdf downloaded by whchowad from http:/petergao.net/ustpastpaper/down.php?course=MATH2033&id=4 at 20160306 07:55:48. Academic use within HKUST only.
Math 2033 (Mathematical Analysis)
Spring 2015
Final Examination (Du
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 2007
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. Works (including scratch works) must be shown
legibly to receive credits. Answers alone are worth very little. Calculato
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 201 (Introduction to Analysis)
Lecture 1
Fall 20042005
Final Examination Time Limit : 2 Hours
Directions. You must show work to receive credits. Answers are worth very little. No calculator
is allowed.
Notation: R; Q and
respectively.
N denote the s
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Fall 2007
Final Examination
Directions: This is a closed book exam. Works (including scratch works) must be shown
legibly to receive credits. Answers alone are worth very little!
Notations: R denotes the set of all
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Solution to Math 202 Homework 3 (Spring 20092010)
f(x) f(0)
f 0 (x)
= lim
= lim g(x) = g(0).
x0
x0
x0
x0
1
Solution 2. By mean value theorem, for every x 6= 0, there exists x strictly between x and 0 such that
f(x) f(0) = f 0 (x )(x 0). As x 0, x 0 by th
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Presentation Exercises
Notation. In the following problems, f (n) will denote the composition f f f .

cfw_z
n f0s
1. Let f, g : R R be continuous and f(g(x) = g(f(x) for all x R. Prove that if the equation
f (2) (x) = g(2) (x) has a solution, then f(x)
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202(Introduction to Real Analysis)
Spring 20092010
Homework #4 Due Monday, May 10, 2010 at noon
Be sure to write your name (as shown on your student ID card) and your tutorial
session number on the homework! Show work. Answers are worth very little.
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 2008
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. Works (including scratch works) must be shown
legibly to receive credits. Answers alone are worth very little. Calculato
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 2009
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. For every problem of this exam, detailed
written works supported by correct reasons must be shown legibly to receive
cre
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
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Multivariable calculus
MATH 2023

Fall 2015
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Multivariable calculus
MATH 2023

Fall 2015
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The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
(MATH2023)[2013](s)midterm~=c5ypu^_91087.pdf downloaded by whchowad from http:/petergao.net/ustpastpaper/down.php?course=MATH2023&id=0 at 20150921 09:38:22. Academic use within HKUST only.
(MATH2023)[2013](s)midterm~=c5ypu^_91087.pdf downloaded by whcho
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 20092010
Homework # 3 Due Monday, March 8, 2010 at 11:30am
Be sure to write your name (as shown on your student ID card) and your tutorial
session number on the homework! Show work. Answers are worth very l
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 2010
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. For every problem of this exam, detailed
written works supported by correct reasons must be shown legibly to receive
cre
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Fall 2008
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. Works (including scratch works) must be shown
legibly to receive credits. Answers alone are worth very little. Calculators
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 201 (Introduction to Analysis)
Spring 20022003
Lectures 1,2,3
Time Limit: 120 Minutes
Final Examination
Remarks. You must show work to receive credits. Answers alone are worth very little. The
symbols R and Q denote the set of all real numbers and t
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Spring 2006
Final Examination (Duration: 120 minutes)
Directions: This is a closed book exam. Works (including scratch works) must be shown
legibly to receive credits. Answers alone are worth very little. Calculato
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
Math 202 (Introduction to Real Analysis)
Fall 20092010
Homework # 3 Due Friday, December 4, 2009 at 11:30am
Be sure to write your name (as shown on your student ID card) and tutorial
session number on the homework! Show work. Answers are worth very littl
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
(MATH2033)[2015](s)midterm~hrtin^_65236.pdf downloaded by whchowad from http:/petergao.net/ustpastpaper/down.php?course=MATH2033&id=6 at 20160306 07:55:50. Academic use within HKUST only.
Math 2033 (Mathematical Analysis)
Spring 2015
Midterm
Directions:
The Hong Kong University of Science and Technology
Multivariable calculus
MATH 2023

Fall 2015
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