|Calculus Exploration 1
1. Use the following applet to explore the concept of "limit of a function." There are three related notions of limit: limiting value of f(x) as x approaches a from the left, limiting value of f(x) as x approaches a from the right, and limiting value of f(x) as x approaches a from both sides. Use the applet to try to come up with (write down) a definition for each of these concepts.
2. Apparently, a function is "continuous" if its graph has no "holes" or "breaks." Use the applet to also come up with (write down) a definition of continuous function on an interval, that employs the concept and definition of limit that you came up with in 1. above.
Acknowledgement: The above applet is a modified version of Limit.java developed by Tom Kiffe at Texas A & M University. We are grateful to him for making this applet available to be used and modified.