Consider the following for the two (02) items that follow: Let the function f(x) = [x] , where [ ] is the greatest integer function and g(x) = |x| . What is _ x 0 f(x) g(x) equal to?

Step-by-step solution

The given functions are f(x) = [x] and g(x) = |x| . To find _ x 0 f(x) g(x) , we evaluate the left-hand limit (LHL) and right-hand limit (RHL) at x = 0 . For the right-hand limit ( x 0^+ ): When 0 _ x 0^+ [x] |x| = _ x 0^+ 0 x = _ x 0^+ 0 x = 0 For the left-hand limit ( x 0^- ): When -1 _ x 0^- [x] |x| = _ x 0^- (-1) -x = _ x 0^- - 1 -x = _ x 0^- 1 x = - Since the left-hand limit and right-hand limit are not equal, the limit does not exist.