1. Limits!

2. ~Definition~ Must be the same from both sides to exist intended height that the graph reaches as x approaches a specific value “c”

3. Left hand limits

4. Where? From the negative x-values From the left

5. Right Hand Limits

6. Where? From the positive x values From the right

7. The limit does not exist!

8. When? Jump discontinuity Infinite discontinuity Discontinuity on an interval

9. Substitution

10. How do I find the limit? Primary method of finding the limit Substitute “c” into your normal equation Example: Review packet 2. In this example, the “c” value is 2 Substitute 2 in for all of the x values, so that the now becomes and the becomes Simplify the above equation, so that you add the terms inside the quantity

11. Simplification

12. How do I find the limit? Use when substitution doesn’t work Look to factor and then simplify Example : Review packet 40. Define f(-2) to make f(x) continuous at x=-2 In order to make the graph continuous, look to factor the top quantity. The top equation factors into , because when you multiply these two together, you get the full equation in the original numerator. There is an quantity in both the numerator and the denominator, so you can cancel them out. You are then left with the quantity

13. Table of Values

14. How do I find the limit? When all else fails, use table of values! Also, look at graph Example: 5. X -2 -1 0 1 2 Y .25 1 ERROR 1 .25