THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineering
Additional Exercise III
1. Consider the following limit of Riemann sum of a function f on [a, b]. Identify f
and express the limit as a denite integral, where
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Selected Solutions to Weekly Exercise 3
2. Construct an upper bound and a lower bound of
5
.
9 4 sin 2x
Solution:
1
4
sin 2x
4 sin 2x
1
4
13 9 4 si
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 4
Due Date: November 16, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 3
Due Date: October 28, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on h
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 6
Due Date: December 6, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on h
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of Quiz 2
Name:
Student No.:
Class:
Final Result:
1. Answer all questions. Please show the work with as much detail as possible f
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Homework 1
Due Date: September 18, 2014
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Homework 6
Due Date: 2nd December 2014
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2014)
Suggested Solution to Coursework 5
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on hone
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Coursework 1 solution
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academic work, and o
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Pre-coursework Exercise 5
1. (a) Factor theorem states that if P (x) is a polynomial and P (a) = 0, then x a
is a factor of P (x).
By using factor th
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Weekly Exercise 3
1. Fill in the blanks and construct an upper bound and a lower bound of
1
cos
1
4 cos
4
7 + 4 cos
11
1
11
1
7 + 4 cos
3
11
3
7
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Pre-coursework Exercise 4
1. Compute the derivative of each of the following function at the given point by using
the formal definition (first princi
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested Solutions to Extra Exercise 4
If you find any errors/typos, please email them to:
[email protected]
Here C and C are an arbitrary c
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of Coursework 7
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academ
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Suggested solutions of coursework 6
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academ
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Solution to Pre-coursework Exercise 6
1. Resolve the following expressions into partial fractions.
5
A
B
+
)
+x6
x+3 x2
5
1
1
Ans: 2
=
x +x6
x2 x+3
1
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Weekly Exercise 2
1. A sequence cfw_an is defined recursively by the following equations:
a1 = 3
and
an+1 =
an + 1
for n 1.
2
Write down the first 5
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Coursework 2 solution
Student No.:
Name:
Class:
I acknowledge that I am aware of University policy and regulations on honesty
in academic work, and o
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Selected Solutions to Weekly Exercise 1
If you find any errors or typos, please email them to: [email protected]
1. Describe the elements in
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Solution to Weekly Exercise 2
If you find any errors or typos, please email them to: [email protected]
Note: If you find any discrepancy betw
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2015)
Weekly Exercise 1
1. Describe the elements in the following sets.
(e.g 1) (, 2) [4, ) = the set of all real numbers x such that x < 2 or x 4;
(e.g 2)
j;1l '7J
-;r;
1~
Not to be taken away
- 1\ (#
T;,
10
:t ~ tf .x.*~
Page 1 of 6
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Copyright Reserved
The Chinese University of Hong Kong
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Course Examination 1st Tenn, 2013-14
Course Code
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Copyright Reserved
The Chinese University of Hong Kong
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liJ:.~JfJl#g:1t
Course Examination 1st Term, 2012-13
[email protected],!t.&.tlJfi
Course Code & Title
CALCULUS FOR ENGINEERS
MATH1510B
*r8'
Calculus for Engineers
Jeff Chak-Fu WONG1
August 2015
1 Copyright
c 2015 by Jeff Chak-Fu WONG
2
Contents
Antiderivatives
19.1 Introduction . . . . . . . . . . . . .
19.2 Integration: Integral of a function .
19.3 Indefinite valuedness of integration.
19.4
Lecture Note 13
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
[email protected]
MATH1020
General Mathematics
Produced by Jeff Chak-Fu WONG
1
T HE C ROSS P RODUCT
HE
C ROSS P RODUCT
2
Find the Cross Product of Two Vec
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Quiz 1
Name:
Student No.:
Class:
Final Result:
1. Answer all questions. Show work to justify all answers.
2. The quiz lasts 40 minutes.
3. If you fin