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6.3.5 Study Project: Satisfying requirements on limits Barbara A. Shipman, Active Learning Materials for a First Course in Real Analysis
 

Summary: 
6.3.5 Study Project: Satisfying requirements on limits
Barbara A. Shipman, Active Learning Materials for a First Course in Real Analysis
www.uta.edu/faculty/shipman/analysis. Supported in part by NSF grant DUE-0837810

Study Project: Satisfying requirements on limits

In this study, it will be helpful to refer to the definitions of limits constructed in Discovery
Exercise: Other types of limits of functions.

1. Functions with a limit on only one side

a) In previous work, we have seen that a function that is not defined on values greater than p
cannot have a right-hand limit at p. Use this observation to construct a function that has a left-
hand limit at 5 but not a right-hand limit at 5.

b) Suppose we now wish to consider functions defined on an open bounded interval around 5.
Find an unbounded function f : (0,10) that has a left-hand limit but not a right-hand limit.

c) If possible, find a bounded function g : (0,10) that has a left-hand limit but not a right-

  

Source: Ambartsoumian, Gaik - Department of Mathematics, University of Texas at Arlington

 

Collections: Mathematics