1. Warmup – No calculator 4) Find the average speed in ft/sec of a ball modeled by over the time period [2,6] (feet

2. 2.2 Limits Involving Infinity

3. Make a table using your calculator xf(x) 1 10 100 1000 Lets push the value of x towards infinite

4. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if: or

5. Example 1: This number becomes insignificant as. There is a horizontal asymptote at 1.

6. Example 2: Find: When we graph this function, the limit appears to be zero. so for : by the sandwich theorem:

7. Example 3: Find:

8. Infinite Limits (Vertical Asymptotes): As the denominator approaches zero, the value of the fraction gets very large. If the denominator is positive then the fraction is positive. If the denominator is negative then the fraction is negative. vertical asymptote at x =0.

9. Evaluate without a calculator

10. Determine Vertical Asymptotes and evaluate each limit

11. Example 4: The denominator is positive in both cases, so the limit is the same.

12. Limits approaching infinite……. aka… HA

14. Example: Sketch a function f(x) that has all of the following properties:

15. The end p. 71 (1-8, 9-21 odd, 47-49)