MA2001 Test 1 Semester A, 2016/2017
Name: Student ID:
Answer ALL questions. (Full marks: 40) Total Marks: Q1: _w Q2: ._
4 O 1
Question 1 (20 marks) Diagonalize the matrix A = (0 3 0) by the following steps.
i) (4 marks) Find the eigenvalues ofA.[Hint;2/1
Illustration on Partial Derivatives
Geometric Interpretation of
f
y
The value f y (a, b ) is the slope of the line tangent at P(a, b, c ) to the ycurve through P on the surface z = f ( x, y ) .
Geometric Interpretation of
f
x
The value f x (a, b ) is the
MA2170 Exercise on Chapter 3
1.
(a)
(c)
(e)
(g)
(h)
(i)
(j)
Vectors
r s
r r s r
It is given that a , b are vectors in R3 with a 0 , b 0 .
Determine whether each of the following is True of False.
r r r r
r3
a+b a + b
(b)
a >0
r
s
r r
proj ar b is parallel
MA1200
Chapter 2
1
Calculus and Basic Linear Algebra I
Sets and Functions
Set Notation
A set is a collection of distinct objects called elements or members of that set. For example,
A 1, 2,3, 4,5 is a set and a list of all its elements is given. In genera
Chapter 2 part 1
Review of Motion Along
a Straight Line
Topics for Chapter 2 part 1
straightline motion in terms of velocity and acceleration
average and instantaneous velocity and average and
instantaneous acceleration
Understanding of graphs of posi
MA1201 Calculus and Basic Linear Algebra II
Lecture Note 2
Integration Technique
1
MA1201 Calculus and Basic Linear Algebra II
Lecture Note 2: Integration Technique
In this Chapter, we shall discuss some important technique in evaluating integrals:
Metho
MA1301
Chapter 1
Calculus and Basic Linear Algebra II
Vector Algebra
1 Review of Basic Ideas (p.1 p.8)
In engineering and science, physical quantities which are completely specified by their magnitude (size)
are known as scalars. Examples are: mass, tempe
MA1201 Basic Calculus and Linear Algebra II
Lecture Note 6
Matrix, Determinant and System of Linear Equations
1
MA1201 Calculus and Basic Linear Algebra II
Lecture Note 6: Matrix and Determinant
Basic Definition of Matrices
A
matrix, denoted by
the form
,
CITY UNIVERSITY OF HONG KONG
Course code and title : MA1200 Calculus and Basic Linear Algebra I
Session 2 Semester B, 2014/2015
Time allowed : Two hours
This paper has SEVEN pages (including this cover page).
Abn’ef table of derivatives is attached on p
CITY UNIVERSITY OF HONG KONG
Course code and title : MAIZGO Calculus and Basic Linear Algebra I
Section C61
Test 1
Session : SemesterA, 2014/2015
Time : 19:00  20:00, 7 October 2014 (Tuesday)
Time allowed : 1 hour
This paper has TWO pages (inctuciing thi
CITY UNIVERSITY OF HONG KONG
Course code and title : MA1200 Calculus and Basic Linear Algebra I
Section CA1, CE}, CC1 and CD1
Test 1
Session : Semester A, 20141201 5
Time : 15:00  16:00, 3 October 2014 (Wednesday)
Time allowed : 1 hour
This paper has TWO
2013 Sem A Exam Answer
1
1a) lim ln(1) = lim
=0
=0
lim
(1 )
(ln(1)
=1
1
=0 1
1
1b) f(x) = 3
1
1
3 03
lim
0
=0
= lim
=0
1
1
3
1
= 0 = Does not exist.
2a) = sin 2
d
d
= 2cos 2
d2
d 2
d3
d 3
= (1)(2)2 sin 2
= (1)(2)3 cos 2
d
d
d
d
2b)
= (1) (2) sin
.Mmeﬂ,déﬁ ewﬂﬁﬁiéaﬁ ﬂute.
Question 1
(a) Let 6 be an angle lies between 180° and 270°, and cost? = mils». Without using a calculator,
ﬁnd the values of
(i) 4mg + 25$ir16 ,
. 9
(n) c053.
(b) Express (203: m ﬁsinx in the form Roos(x +a), where R > 0 and 0 <
MA1200 Calculus and Basic Linear Algebra
Lecture Note 6
Limits
1
MA1200 Calculus and Basic Linear Algebra
Lecture Note 6: Limits
Motivation of Limit
We consider the following function
( )
The function ( ) is not defined at
since the denominator equals to
Semester A, 201516
MA1200
Calculus and Basic Linear Algebra I
Chapter 5
Dr. Emily Chan
Page 1
Semester A, 201516
MA1200
Calculus and Basic Linear Algebra I
Chapter 5
Exponential Functions
The exponential function with base
is defined by
( )=
where the c
MA1201 Calculus and Basic Linear Algebra II
Solution of Problem Set 1 Basic Concept in Integration
Problem 1
(a)
(b)
(
)
(
(c)
(d)
(e)

)
(f)
Problem 2
(a)

 
 
(b)
(c)
(d)
(e)
1
(f)
We use method of partial fraction and decompose the integrand as
Page 1 of 80
MA1201 Calculus and Basic Linear Algebra II
Chapter 4
Vector Algebra
Page 2 of 80
Introduction
We use numbers (real numbers) to describe a lot of things (e.g. temperature, price of
products, your GPA, your achievement in Candy Crush Saga etc.
Page 1 of 72
MA1201 Calculus and Basic Linear Algebra II
Chapter 3
Application of Integration
Page 2 of 72
Application of Integration
1. Geometric Application
Area of region bounded by curves and / or axes (pp. 317)
Volume of a solid generated by revol
Page 1 of 125
MA1201 Calculus and Basic Linear Algebra II
Chapter 2
Integration Technique
Page 2 of 125
In this Chapter, we shall discuss some important technique in evaluating integrals:
Method of Substitution (pp. 3=37)
Integration by parts & Reductio
Page 1 of 60
MA1201 Calculus and Basic Linear Algebra II
Chapter 1
Basic Concept of Integration
Page 2 of 60
What is integration?
Roughly speaking, integration is the reverse process of differentiation: Given a
function (), we would like to find a (differ