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Copyright © Houghton Mifflin Company. All rights reserved. 71-7
Theorem 1.10 The Existence of a Limit
Copyright © Houghton Mifflin Company. All rights reserved. 81-8
Definition of Continuity on a Closed Interval and Figure 1.31
Copyright © Houghton Mifflin Company. All rights reserved. 91-9
Theorem 1.11 Properties of Continuity
Copyright © Houghton Mifflin Company. All rights reserved. 101-10
Theorem 1.12 Continuity of a Composite Function
Copyright © Houghton Mifflin Company. All rights reserved. 111-11
Theorem 1.13 Intermediate Value Theorem
Copyright © Houghton Mifflin Company. All rights reserved. 131-13
Definition of Infinite Limits and Figure 1.40
Finding Vertical Asymptotes
• Determine all vertical asymptotes of the graph.
A) B) C)1( )2( 1)
f xx
2 1( )2 1xf xx
( ) cotf x x
Copyright © Houghton Mifflin Company. All rights reserved. 191-19
Theorem 1.15 Properties of Infinite Limits
Determining Limits
• Because
20 0
20
1lim1 1 and lim , you can write
1lim 1 Property 1, Theorem 1.15
x x
x
x
x
Determining Limits
• Because
0 0
0
lim 3 3 and lim cot , you can write
lim 3cot Property 2, Theorem 1.15
x x
x
x
x
Determining Limits
• Because
2
1 1
2
1
lim 1 2 and lim cot , you can write
1lim 0 Property 3, Theorem 1.15
cot
x x
x
x x
xx
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