Class Notes – 9/24/07
We discussed the homework, did Exploration 2-2, and used the delta-epsilon applet online (on Mrs. Evrard’s webpage).
Informal Definition of Limit – The limit of a function f as x approaches c is the y-value f(x) stays close to when x is kept close enough to c but not equal to c.
Shortened Definition of Limit -
if and only if
for any number 
,
there is a number 
such that
if x is within 
units of c (but 
),
then f(x) is within 
units of L.
Note – In order to be within epsilon units of L, you must take the smaller of the two deltas.
Limit Theorems
Limit of Product of Two Functions:
Example:
Other theorems include:
Limit of a Sum of Two Functions
Limit of a Quotient of Two Functions
Limit of a Constant Times a Function
Limit of an Identity Function
Limit of a Constant Function
Limit of a Composite Function
These theorems follow the same guidelines as the limit of a product of two functions. They can be found and explained in more depth on page 48.
The homework for Wednesday is to do problems 7a, 7b, 9a, 9b, and all the Q’s on page 49.
