UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE : MATH1102
ASSESSMENT : MATH 1 1 023
PATTERN
MODULE NAME : Analysisz
DATE : 31 -May-11
TIME : 14:30
TIME ALLOWED : 2 Hours 0 Minutes
2010311MATH11UEB-UUI-EXAM-19?
@2010 University Cuf
UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE : MATH110I
ASSESSMENT : MATH11D1B
PATTERN
MODULE NAME : Analysis1
DATE : 20-May-11
TIME : 14:30
TIME ALLOWED : 2 Hours 0 Minutes
2010311-MATH11U1B-OU1-EXAM-204
@2010 University (Damag
University College London
DEPARTMENT OF MATHEMATICS
MidSessional Examinations 2010
Mathematics 1101
Friday 15 January 2010 2.30 4.30 or 4.00 6.00
All questions may be attempted but only marks obtained on the best four solutions will
count
The use ofan ele
UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE
MATH1101
ASSESSMENT
PATTERN
MATH1101A
MODULE NAME
Analysis 1
DATE
28-Apr-10
TIME
14:30
TIME ALLOWED
2 Hours 0 Minutes
2009/1 0-MATH11 01A-001-EXAM-223
2009 University College London
T
University College London
DEPARTMENT OF MATHEMATICS
Mid-Sessional Examinations 201]
Malhemalics 110]
Wednesday I2 January 201] 2.30 - 4.30
AH questions may be anempted but only marks obtained an the best four solutions will
count
The use ofan electronic c
University College London
DEPARTMENT OF MATHEMATICS
Mid-Sessional Examinations 2009
Mathematics l 101
Wednesday 14 January 2009 2.30 4.30
All questions may be attempted but only marks obtained on the best four solutions will
count
The use of an electronic
University College London
DEPARTMENT OF MATHEMATICS
Mid-Sessional Examinations 2008
Mathematics 1101
Monday 7 January 2008 11.30 1.30 or 1.15 ~ 3.15
All queslions may be attempted but only marks obtained on [/76 bes/ four so/u/ions will
(01117].
The use
UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE
:
MATH11O1
ASSESSMENT
PATTERN
:
MATH11O1A
MODULE NAME
: Analysis
DATE
:
TIME
: 10:00
TIME ALLOWED
:2Hours0Minutes
2007/08-MATH
11
01
1
09-May-08
4-001 -EXAM-212
@2007 University Colle
/
University College London 1 1
DEPARTMENT OF MATHEMATICS J M 07
Mid-Sessional Examinations 2007
Mathematics 1101
Friday 12 January 200711.30 1.30 or 12.15 2.15
All questions may be attempted but only marks obtained on the best four solutions will
count
T
UNIVERSITY COLLEGE LONDON
University of London
EXAMINATION FOR INTERNAL STUDENTS
For the following qualifications :B. Sc.
M. Sci.
Mathematics MllA:
COURSE
Analysis 1
CODE
:
MATHMllA
:
0.50
DATE
:
02-MAY-02
TIME
:
14.30
:
2 hours
UNIT
TIME
VALUE
ALLOWED
02
UNIVERSITY COLLEGE LONDON
P
University of London
EXAMINATION FOR INTERNAL STUDENTS
For The Following Quafifications:-
B.Sc.
M.ScL
M a t h e m a t i c s M11A: Analysis I
COURSE CODE
:
MATHM11A
UNIT VALUE
:
0.50
DATE
:
19-MAY-03
TIME
:
14.30
TIME ALLOWED
:
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) Let cfw_sin be a sequence of real numbers.
(i) Dene the statement cfw_ztn is a C
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) Consider a function f : R R and a point x0 R.
(i) Dene, in terms of and , the me
UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE : MATH1101
ASSESSMENT : MATH1101B
PATTERN
MODULE NAME : Analysis1
DATE : 15-May-12
TIME : 14:30
TIME ALLOWED : 2 Hours 0 Minutes
2011/12MATH1101B-OO1-EXAM-197
2011 University College
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) Consider a function f : R R and a point x0 R.
(i) Dene, in terms of and , the me
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) Consider a function f : R R and a point x0 R.
(i) Dene, in terms of and , the me
University College Lendon
DEPARTMENT OF MATHEMATICS
Mid-Sessional Examinations 2012
Mathematics 1101
Wednesday 11 January 2012 2:30 4:30
All questions may be attempted but only marks obtained on the best four solutions will
count
The use ofan electronic c
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) State the denition of the derivative of a function f : (0, +) R at the
point x0
l
UNIVERSITY COLLEGE LONDON
\
University of London
EXAMINATION FOR INTERNAL STUDENTS
For The Following Qualifications:-
I
B.Sc.
M.Sci.
Mathematics M11A: Analysis I
COURSE CODE
:
MATHM11A
UNIT VALUE
:
0.50
DATE
:
04-MAY-04
TIME
:
14.30
TIME ALLOWED
:
2 Hou
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use of an electronic calculator is not permitted in this examination.
1. (a) State the denition of convergence of a sequence to a number E E R.
(b) Given two
University College London \ \ H l U \
DEPARTMENT OF MATHEMATICS
Mid-Sessional Examinations 2006
Mathematics M] IA
Wednesday I l January 2006 1.30 - 3.30
All questions may be attempted but only marks obtained on the best four solutions will
count.
The use
UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULECODE
MATH1101
MODULENAME
Analysis 1
DATE
14-May-07
TIME
14:30
TIME ALLOWED
2 Hours 0 Minutes
2006/07-MATH1101A-001-EXAM-225
2006
University College London
TURNOVER
All questions may be atte
Problem Sheet 2 for 6401 Due Monday 27 Oct 2008, at the Problem Class 1. Dierentiate the following functions (a) f (x) = (b) f (x) =
7esin(x ) +3x ; tan(cos x) 3x2 +7 arcsin x+arctan x 3
2
;
(c) f (x) = [(1 + 1/x)1 + 1]1 .
2 1+x2
2. Find the equation of t
Problem Sheet 3 for 6401 Due Monday 10 Nov 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. For the following functions, nd the critical values and local extrema (maxima or minima). Describ
Problem Sheet 4 for 6401 Due Monday 17 Nov 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. We dene
1
N
x dx = lim
a
N
xa dx,
1
if the limit in the right-hand side exists (and is nite). Fi
Problem Sheet 5 for 6401 Due Monday 24 Nov 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. Prove the following identities for hyperbolic functions: (a) cosh(2x) = 2 cosh2 x 1; (b) sinh(2x)
Problem Sheet 6 for 6401 Due Monday 1 December 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. Compute the following indenite integrals: (a) (b) (c)
1 dx; x2 4x2 1 dx; 4+x2 x dx. x2 9
2
2.
6401 Problem sheet 7 Due on Monday 8 December at the problem class (1) Find the Taylor series at x = 0 of the following functions: (a) cos(3x); (b) cos2 x; (c) (d)
1 53x ; 3 (1x)3 .
2008
(2) Find the Taylor series at x = 1 of the following functions: (a)
Math 2220 Section 2.6 :
Problem Set 3 Solutions
Spring 2010
4. Calculate the directional derivative of the function f (x, y ) = 1/(x2 + y 2 ) in the direction of the vector u = i j = (1, 1) at the point (3, 2) . 1 Solution. First normalize u to get a unit