Le c t u r e3 | 1
Chapter 1 Limits and Continuity
Outline 7. Infinite limits and Limits at
Le c t u r e3 | 2
7. Infinite Limits Rule provided
and
provided
and
Le c t u r e3 | 3
EX Show that
Remark For infinite limits, the quotient law and prelim. algebra cannot be used.
Le c t u r e3 | 4
EX (One-sided infinite limits) Evaluate the limits
Le c t u r e3 | 5
Limits At Def We say that
if the values can be arbitrarily close to by taking large enough.
Le c t u r e3 | 6
Def We say that
if the values can be arbitrarily close to by taking small enough.
Le c t u r e3 | 7
EX Find the limit
Le c t u r e3 | 8
Def If either
then the horizontal line
is called a horizontal asymptote of the graph
Le c t u r e3 | 9
Remark
1. All limit laws and facts can be applied.
2. We shall use the fact that
and the limit laws
Le c t u r e3 | 10
EX Find the infinite limits, limits at , and the asymptotes for the function whose graph is shown below.
Le c t u r e3 | 11
EX (Divide by highest power of ) Evaluate
Le c t u r e3 | 12
EX (Do rationalization first) Evaluate
Le c t u r e3 | 13
EX ( ) Evaluate
Le c t u r e3 | 14
Def We say that
if the values of can be arbitrarily large (resp. small) as is large enough. We say that
if the values of can be arbitrarily large (resp. small) as is small enough.
Le c t u r e3 | 15
EX Find the limit
Le c t u r e3 | 16
EX Find
Le c t u r e3 | 17
EX Find