MATH1851 Lecture Notes
Prepared by Professor K. M. Tsang
based on `Introduction to Calculus and Differential Equations' by Pearson
Chapter 1
Limits and Continuity
The number in [ ] refers to the page number of our textbook
Eg. 1, 2 [4] An rock falls from

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 3
The number in [
Applications of Derivatives
] refers to the page number of our textbook
Theore

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 2
The number in [
Dierentiation
] refers to the page number of our textbook
Denition [67] The de

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 5
The number in [
Integration
] refers to the page number of our textbook
5.1 Area under a curve

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 7
Transcendental Functions
7.5 Indeterminate Forms and L Hpitals Rule
o
Theorem 5 - L Hpitals Ru

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 6.
The number in [
Applications of Definite Integrals
] refers to the page number of our textboo

MATH1851 Lecture Notes on Calculus (prepared by Prof. K. M. Tsang)
based on `Introduction to Calculus and Differential Equations' published by Pearson
Chapter 8
Techniques of Integration
Indenite Integral - Denition [184, 189] A function F is an antideriv

MATH1851 Tutorial 6
1. (a) Show that
a
0
f (x) dx =
05-10-2015
a
0
f (a x) dx.
(b) Use part (a) to evaluate
2
0
sin x
dx .
sin x + cos x
Answer.
(a) Let t = a x, then dt = dx; x = 0 t = a, x = a t = 0, so
a
0
a
a
f (a x) dx =
f (t) (dt) =
f (t) dt =
f