1. Product and Composition of Limits

2. Properties of Limits
These are only true IF EACH LIMIT EXISTS and THEY ARE REAL NUMBERS and do not create an indeterminate form!

3. What if some limits don’t exist?
Later on, we will learn methods to deal with limits if they create indeterminate forms 0/0 etc.

4. Example 1
Solution:
Graph of f(x)
Left hand limit:
Right hand limit:
The left and right hand limits are different so the limit DNE.

5. Example 2
Graph of f(x)
Graph of g(x)
Solution:
Left hand limits:
Right hand limits:
The left and right hand limits are both 0 so the limit is 0.

6. Composition of Limits

7. Graph of f(x)
Graph of g(x)

8. Graph of g(x)
Graph of f(x)

9. Example 5
Graph of g(x)
Graph of f(x)

10. Example 6
Solution:
Graph of f(x)

11. Example 7
Graph of f(x)
Graph of g(x)
Solution:

12. Example 8
Solution
Graph of f(x)
Graph of g(x)