NDA 2 2025 Maths, question 73

Topic: Differential calculus

Passage · Q73 to Q75

Consider the function $f(x)=x|x|$ .

Q73

What is $\underset{x\to -1}{\lim }f(x)$ equal to?

(a) $-1$ Correct answer
(b) $0$
(c) $1$
(d) Limit does not exist

Solution.

Answer: (a) $-1$

For negative x, |x|=−x and f(x)=−x².
The function is continuous near −1, so the limit is −(−1)²=−1.