MCS 118 Fall 2013
September 26, 2013
MCS 118, 9/26/13
Slide #2
Announcements
• Quiz next Monday. If you need accommodations, see
me.
• No office hours for BK on Friday
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118 9/26/13
Slide #3
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
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118, 9/26/13
Slide #4
Graph these functions
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118, 9/26/13
Slide #5
Left-hand and right-hand limits
• What they are
• How are they related to the (two-sided) limits we’ve
been talking about
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118, 9/26/13
Slide #6
Continuous functions
• Continuous at a point
• Continuous on an open interval
• Continuous on a non-open interval
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118, 9/26/13
Slide #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
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu
MCS 118, 9/26/13
Slide #8
Coming up:
• Quiz on Monday next week, no class on Tuesday
GUSTAVUS ADOLPHUS COLLEGE
gustavus.edu