Introduction to Limits
Section 1.2
What is a
limit?
A Geometric Example
Look at a polygon inscribed in a circle
As the number of sides of the polygon
increases, the polygon is getting closer to
becom
Continuity and One-Sided Limits
Lesson 2.4
2
3
4
Intuitive Look at Continuity
A function without
breaks or
jumps
The graph can be
drawn without lifting the pencil
5
Continuity at a Point
A function
3.1
Derivatives
Great Sand Dunes National Monument, Colorado
Photo by Vickie Kelly, 2003
Greg Kelly, Hanford High School, Richland, Washington
lim
h 0
f a h f a
h
We write:
f
is called the derivative
Continuity
2.4
Most of the techniques of calculus require that functions
be continuous. A function is continuous if you can draw it
in one motion without picking up your pencil.
A function is continuo
The derivative as the slope of the
tangent line
(at a
point)
What is a derivative?
A function
the rate of change of a function
the slope of the line tangent to
the curve
The tangent line
single poi
What is calculus?
What do you learn in a calculus class?
How do algebra and calculus differ?
You will be able to answer all of these
questions after you finish the course.
10.1 Introduction to Lim
Chapter 2: Limits and Continuity
Section 2.1 The Limit Process (An Intuitive Introduction)
a. The Limit Process
b. Area of a Region Bounded by a Curve
c. The Idea of a Limit
d. Example
e. Illustration