1. MCS 118 Fall 2013 September 26, 2013

2. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu Announcements Quiz next Monday. If you need accommodations, see me. No office hours for BK on Friday MCS 118, 9/26/13Slide #2

3. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu Today’s schedule Graph three functions and look at limits Left-hand and right-hand limits Continuous functions Types of discontinuous functions Intermediate value theorem MCS 118 9/26/13Slide #3

4. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu MCS 118, 9/26/13Slide #4 Graph these functions

5. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu MCS 118, 9/26/13Slide #5 Left-hand and right-hand limits What they are How are they related to the (two-sided) limits we’ve been talking about

6. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu MCS 118, 9/26/13Slide #6 Continuous functions Continuous at a point Continuous on an open interval Continuous on a non-open interval

7. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu MCS 118, 9/26/13Slide #7 Analyze a function for continuity Graph it Look at left-hand and right-hand limits If they’re equal, then the function has a removable discontinuity If they both exist, but aren’t equal, then the function has a jump discontinuity (which is non- removable) Otherwise, there’s a non-removable discontinuity

8. GUSTAVUS ADOLPHUS COLLEGEgustavus.edu Coming up: Quiz on Monday next week, no class on Tuesday MCS 118, 9/26/13Slide #8