Introduction to Limits: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 01 Page 1
Introduction to Limits
The limit of a function is concerned with the behaviour of a function near a given point. Wha
Limits Involving Innity: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 04 Page 1
Limits Involving Innity
Lets start with what we mean when we say x f (x) = L or lim f (x) = L.
lim
x
We say f (x) h
Module 1 Exam: Dr. C. Sean Bohun
Limits and Continuity, Page 1
Registration number:
Module 1 Exam
Instructor: Dr. C. Sean Bohun
Time: 55 Minutes
Instructions:
1. Answer questions on the examination pa
Introduction to Limits II: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 02 Page 1
Introduction to Limits II
In order to compute a limit algebraically, one needs to know what is and more important
The Squeeze Theorem: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 03 Page 1
The Squeeze Theorem
Lets start with a statement of the squeeze theorem.
Theorem 1.1 Suppose g(x) f (x) h(x) and this
is
Module 1 Exam: Dr. C. Sean Bohun
Limits and Continuity, Page 1
Name:
KEY
[16] 1. For each of the following, nd the limit if it exists. Otherwise state that it does not exist and
why.
x+1
.
[2] (a) lim
Strategy to Calculate Limits: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 05 Page 1
Strategy to Calculate Limits
To compute xa f (x):
lim
1. Try to plug the value of a directly into the function
Continuity: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 06 Page 1
Continuity
A function f (x) is said to be continuous at a point a in its domain if the following three properties
hold.
1. lim f
Intermediate Value Theorem: Dr. C. Sean Bohun
Limits and Continuity, Tutorial 07 Page 1
Intermediate Value Theorem
To begin with, lets start with the basic statement of the theorem.
Theorem: If f (x)