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. 0
- C. 1
- D. Limit does not exist
Answer
B. 0
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
Related: Mathematics — Limits · All PYQ Banks