This lecture:
Horizontal asymptotes: a first example.
Horizontal asymptotes
Horizontal asymptotes
A round of the game:
+
M=2
Lets watch a few rounds
Player A.
Player B.
Lets watch a few rounds
Player A.
Well consider how to go about
demonstrating this a b

This lecture: Part 1.
Recall:
Example.
=0.15
=0.20
=0.25
=0.30
=0.35
=0.40
=0.45
=0.50
=0.55
=0.60
=0.65
=0.70
=0.75
=0.80
=0.85
=0.90
Functions can only have one limit
Now that we have a rigorous definition of limit, we can set about
building up the theo

The precise definition of limit.
Recall the idea of limit
?
Recall the intuitive definition we gave earlier.
Right now well:
Play with this definition a bit to get a feeling for what it says.
Then well obtain the precise mathematical definition by
simpl

This lecture.
The definition of and topics related to the important concept
of Continuity.
The definition and first examples.
Important classes of continuous functions:
Polynomials
Rational functions
Trigonometric functions
Exponential functions
U

Andrew Kricker
[email protected]
SPMS building, 4th floor,
office number MAS 04-18.
The textbook
It is:
Calculus
By James Stewart
The international, 7th,
metric edition.
I recommend buying this because:
This course will be based closely on this boo

This lecture.
This lecture we are going to focus on the concept of the
derivative of a function.
Recall why we needed limits
Remember the main motivation for introducing limits?
We discovered we need limits because when we tried to write
down formulas for

This lecture.
This lecture we are going to focus on the calculus of the
trigonometric functions.
Trigonometric functions: the definitions?
Recall the main idea of these functions
Trigonometric functions: the definitions?
The precise definition (wont be te

This lecture.
In this lecture:
Inverse functions. Review of the basic concepts.
Calculus of inverse functions:
o Continuity of the inverse.
o Derivative formula for the inverse function.
Inverse trigonometric functions.
Inverse functions
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