Q223 / 270 · NDA 2025 (Phase 2) · Mathematics
For the following three (03) items:
Consider the function $f(x) = x|x|$.
What is $\lim_{x \to -1} f(x)$ equal to?
Consider the function $f(x) = x|x|$.
What is $\lim_{x \to -1} f(x)$ equal to?
- Correct answerA$-1$
- B$0$
- C$1$
- DLimit does not exist
Solution
Given the function $f(x) = x|x|$.
We need to evaluate $\lim_{x \to -1} f(x)$.
Since $x$ approaches $-1$, $x$ is negative, so $|x| = -x$.
Thus, $f(x) = x(-x) = -x^2$ for $x < 0$.
$\lim_{x \to -1} f(x) = \lim_{x \to -1} (-x^2) = -(-1)^2 = -1$.
Answer: $-1$
We need to evaluate $\lim_{x \to -1} f(x)$.
Since $x$ approaches $-1$, $x$ is negative, so $|x| = -x$.
Thus, $f(x) = x(-x) = -x^2$ for $x < 0$.
$\lim_{x \to -1} f(x) = \lim_{x \to -1} (-x^2) = -(-1)^2 = -1$.
Answer: $-1$
Hence, the correct answer is option: 'A'.