The document discusses limits in mathematics. It defines a limit as the intended height of a function as values get closer and closer to a given number. Examples are provided of evaluating limits, including finding limits of expressions as x approaches 1 and determining whether limits exist or are infinite. Common types of limits like one-sided limits and limits at infinity are also mentioned.

1. 1. Limits
For you, what is a limit?

2. 1. Limits

3. 1. Limits

4. 1. Limits

5. 1. Limits

6. 1. Limits
Let’s work it out for x = 1

7. 1. Limits
Let’s work it out for x = 1

8. 1. Limits

9. 1. Limits
The limit of (x2 - 1)/(x - 1) as x approaches 1 is 2

10. 1. Limits
The limit of (x2 - 1)/(x - 1) as x approaches 1 is 2

11. 1. Limits

12. 1. Limits
"ignoring what happens when you get there, but as
you get closer and closer the answer gets closer and
closer to 2"

13. 1. Limits
"ignoring what happens when you get there, but as
you get closer and closer the answer gets closer and
closer to 2"

14. 1. Limits
Common Sense Definition
A limit is the intended height of a function.

15. 1. Limits
When it is different from different sides.

16. 1. Limits
When it is different from different sides.

17. 1. Limits
When it is different from different sides.

18. 1. Limits
When it is different from different sides.

19. 2. Examples
Find the following limits:

20. 2. Examples
Find the following limits:
=1

21. 2. Examples
Find the following limits:
=1 =DNE

22. 2. Examples
Find the following limits:
=1 =DNE =2

23. 2. Examples
Find the following limits:
=1 =DNE =2 = −∞

24. 2. Examples
True or False:
!
DNE
!
DNE
!
DNE

25. 2. Examples
True or False:
! False
DNE
!
DNE
!
DNE

26. 2. Examples
True or False:
! False
DNE False
!
DNE
!
DNE

27. 2. Examples
True or False:
! False
DNE False
! False
DNE
!
DNE

28. 2. Examples
True or False:
! False
DNE False
! False
DNE True
!
DNE

29. 2. Examples
True or False:
! False
DNE False
! False
DNE True
! True
DNE

30. 2. Examples
True or False:
! False
DNE False
! False
DNE True
! True
DNE False