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- Collections: Mathematics