1. Math 1241, Spring 2014 Section 3.1, Part Two Infinite Limits, Limits “at Infinity” Algebraic Rules for Limits

2. Infinite Limits

4. Examples of Infinite Limits

6. Limits “at Infinity” On the previous graph, what happens to the value of f(x) as x gets “larger and larger?” – On the graph: Further and further to the right. Similar question: what happens to the value of f(x) as x gets “more and more negative?” – On the graph: Further and further to the left. In previous courses, these questions were related to horizontal asymptotes of the graph.

7. Limits “at Infinity”

9. Infinite Limits “at Infinity”

11. Algebraic Rules for Limits

12. Simple Algebraic Examples

14. Exercises

15. Exercise: Rational Functions

16. Solutions

18. Many graphing programs do not detect the “hole in the graph” when x = 2. When our function has a zero denominator, we can try to factor numerator/denominator, and hope that the zero factor cancels. HINT: In this case, the numerator and denominator are zero at x = 2, so there should be a factor of (x-2).

20. An Important Result

21. For more complicated functions, we can often evaluate limits with the following rules (pg. 128)

22. Roots/Fractional Exponents