Question
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?
NDA
Mathematics
Limits
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. - 1
- B. 1
- C. 0
- D. Limit does not exist
Answer
D. Limit does not exist
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.
Related: Mathematics — Limits · All PYQ Banks