Definition of Limit - If f(x) becomes abritrarily close to a unique number L as x approaches a from either side, the limit of f(x) as x approaches a is L. This is written as :
It does not matter what happens what x=a specifically, it only matter what is happening as x appraches a.
WHEN LIMITS DO NOT EXIST:
The limis of f(x) as x approaches c does not exist id any of the following conditions is true.
1. f(x) approaches a different number from the right side of c than from the left side of c.
2. f(x) increases or decreases without bound as x approaches c.
3. f(x) oscillates between two fixed values as x approaches c.
Properties of limits:
12.2 techniques for evalutating limits
Limits of polynomial and rational functions
1. If p is a polynomial function and c is a real numner then the limits of p (x) as x approaches c is p(c)
2. If r is a rational function given by r(x)=p(x)/q(x), and c is a real number such that q(c) doesn't = 0, then the limit of r(x) as x approaches c is = r(c)= p(c)/q(c)
12.4 limits at infinity and limits of sequences
1. "The limit of f(x) as x approaches negative infinity is 
"
2. "the limit of f(x) as x approaches infinity is 
"
LIMITS AT INFINITY
for the rational function f(x)=N(x)/D(x), where
and
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