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1.1 Limits Graphically Name:_________________________
Write your questions and
thoughts here!
Calculus
Notes
What is a limit?
A limit is the __________ a function ______________ from both the left and the right side of a given ___________. Example 1
3
� �
�oxf
x 3lim
3
� � �o
xfx 3lim
3
� � �o
xfx 3lim
3
� � �o
xfx 3lim
3
� � �o
xfx 3lim
Limit: (geeky math definition for Mr. Kelly) Given a function , the limit of as approaches is a real number if can be made arbitrarily close to by taking sufficiently close to (but not equal to ). If the limit exists and is a real number, then the common notation is
→.
What is a one‐sided limit?
A one‐sided limit is the ___________ a function approaches as you approach a given ___________ from either the ______ or ______ side. Example 2
“The limit of as approaches 3 from the left side is 1.” lim
→1
“The limit of as approaches 3 from the right side is 2.” lim
→2
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1.1 Limits Graphically
Write your questions and thoughts here!
NotesExample 3 a. � �
��oxf
x 2lim b. � �
��oxf
x 2lim c. � �
�oxf
x 2lim
d. � �
oxf
x 1lim e. � �
oxf
x 0lim f. � �
�oxf
x 3lim
g. � � �o
xfx 1lim h. � �
�oxf
x 3lim
i. 2
j. 1
When does a limit not exist?
1. 2. 3. Example 4 Sketch a graph of a function that satisfies all of the following conditions.
a. 3 1 b. 4)(lim
3
o
xgx
c. )(lim2
xgx ��o
1
d. is increasing on 2 3 e. )(lim
2xg
x ��o
)(lim2
xgx ��o
Example 5 Write T (true) or F (false) under each statement. Use the graph on the right.
a. � � 1lim1
��oxf
x
b. � � 2lim2
o
xfx
c. � � 1lim1
�oxf
x
d. � � 2lim
1
�oxf
x
e. � � existnot does lim1
o
xfx
f. � � � �xfxfxx �� oo
00
limlim
g. � � existnot doeslim2
o
xfx
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