The limits of a function module01

1. THE LIMITS OF A FUNCTION
Now the concept of limit is fundamental to the study of calculus. A limit is something that can or
cannot be reached but can be possibly calculated. A mathematical limit has characteristics similar to
those of a physical limit. It is the analysis of limit of how function values or outputs change, when inputs
change.
If the values of get closer and closer to number as the values of approaches , we
say that is the limit of as approaches
Read as: the limit of as approaches is
FINDING THE LIMITS OF FUNCTION THROUGHT TABLE OF VALUES
EXAMPLE #1: Determine the .
ALGEBRAIC TECHNIQUES IN FINDING THE LIMITS (LIMIT LAWS)
Let and be real numbers, and let and be functions such that
LIMIT LAWS EXAMPLES
If is a constant, and
𝑓 𝑥
𝑓
𝑓
Using the table of values, it is observed that as 𝑥 approaches 3 form both left and right, 𝑓 𝑥
approaches 11
𝒙 2 2.5 2.9 3 3.1 3.5 4
𝒇 𝒙 10 10.5 10.9 11 11.1 11.5 12

2. [ ] [ ]
If is a polynomial function, then
if [ ] [ ]

3. If is any real number, [ ] [ ]
[ ]