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

Given f(x) = [x] and g(x) = |x| . To find _ x 0 f(x) g(x) , we evaluate the left-hand limit (LHL) and the right-hand limit (RHL). For LHL, as x 0⁻ , [x] = -1 and |x| = -x . _ x 0⁻ f(x) g(x) = _ x 0⁻ ( (-1))(-x) = (- 1)(0) = 0 For RHL, as x 0⁺ , [x] = 0 and |x| = x . _ x 0⁺ f(x) g(x) = _ x 0⁺ ( 0)(x) = (0)(0) = 0 Since LHL = RHL = 0 , the limit exists and is equal to 0 . Answer: 0