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. What
happens at the point is of no concern. To be more pre
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) has limit L as x approaches innity () and write lim f (x
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 paper. Use the back of the paper if extra space is needed
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 importantly what is
not allowed when manipulating limits. For ex
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 true for all x in a neighbourhood of x = a (except per
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 2
x1 x + x + 1
Solution: Just plug in x = 1 to get 2/3
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.
If we get a number or the limit blows up then we are
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 (x) exists. This takes three steps to show in itself.
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) is continuous on a closed interval [a, b] and N is any