Question
For the following three (03) items: Consider the function f(x) = x|x|. What is _ x -1 f(x) equal to?
NDA
Mathematics
Limits
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. -1
- B. 0
- C. 1
- D. Limit does not exist
Answer
A. -1
Step-by-step solution
Given the function f(x) = x|x|. We need to evaluate _ x -1 f(x). Since x approaches -1, x is negative, so |x| = -x. Thus, f(x) = x(-x) = -x^2 for x _ x -1 f(x) = _ x -1 (-x^2) = -(-1)^2 = -1. Answer: -1
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