1. 11.1 Intro to Limits

2. Limit- as you look at both sides of the graph of a function at a specific number, it is the value that the function approaches.

3. The function does not have to be defined at that specific place, it just must approach the same y value as you get closer to x from the left or the right.

4. A. Estimating Limits Numerically
1) We use a table of values close to 2 and look at what is happening to the y values. X
1.9
1.99
1.999 2
2.0001
2.001
2.01
f(X) ?

5. 2) X
-.01
-.001
-.0001
.0001
.001
.01
f(X) ?

6. 3) X
1.9
1.99
1.999 2
2.0001
2.001
2.01
f(X) ?

7. B. Finding Limits Graphically
4) 5) 6)

8. 7) 8) 9) 10) f(0)=

9. 11) f(1)= 12) 13) 14)

10. 15) 16) 17) 18) f(-2)

11. C. Evaluating Limits using Direct Substitution
Direct Substitution- means that you replace the variable with whatever it is approaching.

12. Examples-using direct substitution
19) 20) 21)

13. Wow, this is so much easier, why don’t we do it this way all the time
Wow, this is so much easier, why don’t we do it this way all the time? First, it does not always work as you will see in the next section or even in problems 2 and 3.

14. 22) 23) 24) 25)

15. Homework
Pages #3, 5, odd every other odd