LESSON 2: FINDING LIMITS ANALYTICALLY
Properties of Limits
Some Basic Limits
Let b and c be real numbers and let n be a positive integer.
lim
=
lim =
lim =
Methods to Analyze Limits
1. Direc
LESSON #6: LIMITS AT INFINITY
Consider the "end-behavior" of a function on an infinite interval.
3
%
= %
+1
3
3
as
as
lim
= 3
"#
lim
= 3
#
In the example above, the value of y appr
Product and Quotient Rules
1. The Product Rule:
If a function is the product of two differentiable functions then the derivative is the first
times the derivative of the second plus the second times t
LESSON 3: CONTINUITY AND ONE-SIDED LIMITS
Definition of Continuity
Continuity at a Point:
A function f is continuous at c if the following three conditions are met:
1. () is defined.
2. lim
() exists
LESSON #1: THE DERIVATIVE AND TANGENT LINE PROBLEM
Analytically: The definition of a derivative of f at x is
Graphically: The derivative of a function at a point p is the slope of a tangent line to th
LESSON 1: FINDING LIMITS GRAPHICALLY AND NUMERICALLY
When finding limits, you are finding the y-value for what the function is approaching. This can be
done in three ways:
1.
2.
3.
Make a table
Draw a
LESSON #2: BASIC DIFFERENTIATION RULES AND RATES OF CHANGE
The Constant Rule
The derivative of a constant function is 0. For any real number, c
() = 0
f (x)
x
EX #1: Using the Constant Rule
Function
D
Implicit Differentiation
We have been able to differentiate functions that are solved for y explicitly up to this point. Now we want
to consider functions of the type 2 2 3 + 4 = 2. You can see that i