1
Ch5/MATH0211/YMC/2009-10
Chapter 5. Dierentiation
5.1. Derivatives
In this section, we introduce the concept of a derivative. There are two main interpretations of
derivatives (i) the geometric one is the slope of the tangent line to the graph of a func
MATH 0211: Basic Applicable Mathematics
Suggested Solution for Assignment 2
1. (a)
2x 3
1
f ( x) =
3 2x
if x 2,
if 1 x < 2,
if x < 1.
(b) See supplementary sheet
(c) From the graph we observe that the range is [1, )
(d) No.
b
2. (a) f (x) = a(x2 + a x)
A3/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Assignment 3
Due date : Oct 19, 2009 before 17:00.
Remember to write down your Name, Uni. number and Tutorial Group number.
You are welcome to
A4/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Assignment 4
Due date : Nov 5, 2009 before 17:00.
Remember to write down your Name, Uni. number and Tutorial Group number.
You are welcome to s
MATH0211
Basic Applicable Mathematics
Dr. Yat-Ming Chan
Department of Mathematics
The University of Hong Kong
First Semester 2009-10
Content Outline
1. Pre-Calculus Topics
Sets theory, Permutation and Combination, Functions and Graphs, Composite and
Inver
Ch2/MATH0211/YMC/2009-10
1
Chapter 2. Permutations and Combinations
2.1. The Basic Principle of Counting
In this section we introduce the basic principle of counting. Let us rst consider the following
example.
Example 2.1 Suppose there are two roads conne
1
Ch3/MATH0211/YMC/2009-10
Chapter 3. Functions
3.1. Functions and Graphs
The idea of a function expresses the dependence between two quantities, one of which is given and
the other is the output. A function associates a unique output with every input ele
1
Ch4/MATH0211/YMC/2009-10
Chapter 4. Limits and Continuity
4.1. Limits
The concept of a limit lies at the foundation of calculus. The idea involves the notion of getting
closer and closer to something, but yet not touching it. Limits are used to dene con
357 In Class Work No. 1 First Name_
Last Name _
1. According to US Generally Accepted Accounting Principles, long-lived assets are recorded at:
a.
b.
c.
d.
Market value
Replacement cost
Historical cost
None of the above
2. A company has 20,000 shares auth
A2/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Assignment 2
Due date : Sep 30, 2009 before 17:00.
Remember to write down your Name, Uni. number and Tutorial Group number.
You are welcome to
MATH 0211: Basic Applicable Mathematics
Suggested Solution for Assignment 1
1. (a) The solution set for equation (x 5)(x2 + 1.5x 1) = (x 5)(x 0.5)(x + 2) = 0
is cfw_2, 0.5, 5.
Note that x N is required, thus we have cfw_x N : (x 5)(x2 + 1.5x 1) = 0 =
cfw_
A1/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Assignment 1
Due date : Sep 17, 2009 before 17:00.
Remember to write down your Name, Uni. number and Tutorial Group number.
You are welcome to
1
Ch7/MATH0211/YMC/2009-10
Chapter 7. Integration
7.1. Indenite Integrals
We have studied how to dierentiate a given function f (x) in the last two chapters. Starting with
this section, we would like to know what function we diferentiate to get f (x), or
SE1/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Supplementary Exercise 1
(Chapter 14)
(NOT to be handed in)
3
1. Let A = [2, 3), B = cfw_x R : | x 2| 4, C = (1, 4) Z. Find the following sets
SE1Sol/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Sketched Solutions to Supplementary Exercise 1
3
1. Let A = [2, 3), B = cfw_x R : | x 2| 4 C = (1, 4) Z
Find the following sets
(1) C can a
T1/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Tutorial 1
1. Let
A = cfw_ R : x2 + x + 4 = 0 has two distinct solutions,
B = cfw_ R : x2 + x + 4 = 0 has exactly one solution,
C = cfw_ R : x2
T2/MATH0211/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH0211 Basic Applicable Mathematics
Tutorial 2
1. Show that a linear function f (x) = mx + c, where m = 0, is injective. Find the inverse of
it and show that it is also a linear f
119.
a)
Initilal Outlay of the project
Purchase Price
$1,40,000
.00
Installation Charges
$5,000.00
Additional investment required in inventory
$7,000.00
Total Initial Outlay
$1,52,000
.00
b)
Annual after-tax cash flows
Increase in earnings before interest