7. Integration
Indefinite integrals
Now we consider the reverse of the differentiation: given a function f ( x) , how
can we find another function F ( x) such that F '( x) f ( x) ? We first define the
antiderivative of a function as follows.
Definition 7.
5. Differentiation
Derivative
We begin with the definition of the derivative.
Definition 5.1 Let f : D be a function defined on an interval D .
(a) Given an interior point x0 of D, if the following limit exists
f ( x) f x0
lim
x x0
x x0
(5.1)
then f ( x)
8. Definite integrals
The idea of definite integral starts with completely different background
and motivation from those of indefinite integrals.
It turns out, however, that these two versions of integrals are intrinsically
related by the Fundamental T
Lecture Notes
MAT1001 Calculus I
Dr. Xian Zhou
The Chinese University of Hong Kong, Shenzhen
Overview:
This course teaches fundamental principles and methods of one-variable
calculus with rigorous theory and sophisticated techniques. Topics include:
Infi
Lecture Notes
MAT1002 Calculus II
Dr. Xian Zhou
The Chinese University of Hong Kong, Shenzhen
Overview:
This course is a continuation of Calculus I. Topics include:
Infinite series
Vectors and space
Partial differentiation
Multivariate and iterated in
Tutorial 3
Dr. Grant Rao
September 21, 2015
1. Find the limit of the following:
P
(i) lim nk=1 nk2
n
Solution :
n
X
k
lim
n
n2
k=1
n
1 X
k
= lim 2
n n
1
1 n(n + 1)
n n2
2
n+1
= lim
n 2n
1
= .
2
(ii) lim n + 1 n
= lim
n
1
Solution :
n+1 n
n
( n + 1 n)( n
MAT1002 Calculus II
Information for the Midterm Test
The midterm test is scheduled on Saturday, 19 March 2016, 10:00 12:00am. The test
consists of 20 multiple choice questions and 6 questions, all to be attempted. All multiple
Choice questions and short q
Tutorial 2
January 28, 2016
1.Find the radius of convergence for the following power series.
P
P 3n n
x
(a)
cn x n =
1+6n
Solution: cn =
3n
.
1+6n
Notice that
3n
6n
<
3n
1+6n
<
3n
.
2(6n )
1/n
Hence lim cn = 1/2 by the sandwich rule. So the radius of
n
co