The floor function For any real number x, the floor
Chapter 2, Problem 37(choose chapter or problem)
The floor function For any real number x, the floor function (or greatest integer function) :x; is the greatest integer less than or equal to x (see figure). a. Compute lim xS-1- :x;, lim xS-1+ :x;, lim xS2- :x;, and lim xS2+ :x;. b. Compute lim xS2.3- :x;, lim xS2.3+ :x;, and lim xS2.3 :x;. c. For a given integer a, state the values of lim xSa- :x; and lim xSa+ :x;. d. In general, if a is not an integer, state the values of lim xSa- :x; and lim xSa+ :x;. e. For what values of a does lim xSa :x; exist? Explain. _3 _2 1 2 3 _3 _2 _1 y 1 2 3 x y _ x
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