MA1101R: Answers/Solutions of Exercise 1
(Version: January 29, 2011)
1. (a), (c), (f) are linear equations. (b), (d), (e) are not.
2. (a) is a linear equation. (b) is a linear equation if k = 0. (c) is a linear equation
if k = 0 or 1.
2
3. (a) x = t, y =
MA1100 Homework Set 3 Hints
1. Use ordinary PMI.
(a) In the inductive step, add an additional term to both sides of P (k );
(b) In the inductive step, multiply 9 to both sides of P (k ).
2. Use ordinary PMI.
(a) In the inductive step, try to express f4(k+
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 5 (26/0930/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 4 (12/0916/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 3 (05/0909/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 4
Semester I 2010/11
MA1101R Laboratory 4
Matrix Operations, Eigenvalues and Diagonalization
In this laboratory session, we will learn more matlab commands and apply them
to sol
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 2 (29/0802/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 3
Semester I 2010/11
Transformation Matrices
In this laboratory session, we will use the specially written matlab functions
trans2x2 and trans3x3, to visualize the geometrical e
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 1 (22/0826/08)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 2
Semester I 2010/11
Solving Systems Of Linear Equations
In this laboratory session, we continue to explore working with square matrices, investigate systems of linear equations
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
MA1102R Calculus
Solution to Tutorial 11
Tutorial Part I (Partial)
1
dy
dy
1. (a) Suppose 2 xy
= 1, x, y > 0. Then y
= . Integrate with respect to
dx
dx
2x
x:
1
2
dx y 3/2 = x + C.
y dy =
3
2x
That
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 1
Semester I 2010/11
A Very Brief Introduction to MATLAB
and Matrix Operations
In this laboratory session, we introduce some very basic MATLAB commands for
performing matrix ope
HW4:CommonMistakes/problems/GeneralComments
Q1(d) Some students did not use arrows (in arrow diagrams) but merely straight links to link the
elements in the domain and the co-domain, giving rise to ambiguity.
Q2(c) Many students gave wrong answers for ran
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 6 (03/1007/10)
MA1102R Calculus
Tutorial Part I
This tutorial will be discussed during the e-learning week. The complete solution will be
provided on IVLE. You may post your queries of the tu
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 10 (31/1004/11)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provide
MA1100 Homework Set 2
Semester 1, 2011/2012
Please read:
Do all the problems below and submit on September 16 (Friday) during lecture.
Use A4 size paper. Write your full name, student number and tutorial group
clearly on the rst page of your answer scri
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 9 (24/1028/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
MA1100 Homework Set 2 Hints
1. Use direct proof for (a) and contrapositive proof for (b). For (c), you should
apply (a) and (b) without having to rewrite their proofs again.
2. Use direct proof and denition of divisibility. For (d), you need to use the fa
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 8 (17/1021/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
MA1100 Homework Set 1
Semester 1, 2011/2012
Please read:
This is NOT the same as your tutorial set.
Do all the problems below and submit on September 2 (Friday) during lecture.
Use A4 size paper. Write your full name, student number and tutorial group
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 7 (10/1014/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected questions (indicated by ) from this part will be provided
MA1100 Homework Set 1 Hints
1 There are many possible answers:
(a) Refer to Chartrands exercise Qn 1.7.
(b) One possibility is to use power set of S as the underlying set, and cardinality
in the underlying condition.
(c) Use Z Z as the underlying set.
2 B
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
MA1102R Calculus
Solution to Tutorial 10
Tutorial Part I (Partial)
1. Solving x4 = 8x, we have x = 0 and x = 2. Note that 8x x4 on [0, 2]. Then the area
enclosed by y = x4 and y = 8x is given by
2
x5