12.1 Estimating Limits Graphically

1. Essential Question. How can I find one-sided limits? How can I find infinite limits? 12.1 Estimating Limits Graphically Day 2

2. Left-hand and right-hand limits We write The limit of f(x) as x approaches c from the left is L.

3. Similarly, we write The limit of f(x) as x approaches c from the right is L.

4. Note that if and only if and

5. does not exist because the left and right hand limits do not match! left hand limit right hand limit value of the function Example 1 2 1 1 2 3 4 Find the Following: 0 1 1

6. because the left and right hand limits match. left hand limit right hand limit value of the function Example 2 2 1 1 2 3 4 Find the Following: 1 1 2

7. Limits at infinity

8. Limits at infinity

9. Limits at infinity

10. Example 3 – Find the following limits 1 1

11. Example 4 – Find the following limits A limit of 0 indicates all the medicine will be eliminated from the bloodstream.

12. Example 5 – Find the following limits 1. = -4 = 0 2. 3. 4. DNE

13. Homework:12.1 Day 2 worksheet