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UPSC NDA II 2025 Mathematics Paper

Question Numbers: 73-75

For the following three (03) items:

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

Question : 73 of 120

Marks: +1, -0

What is

\underset{x→-1}{lim}f(x)

equal to?

Solution:

Concept:

The absolute value function

|x|

changes the sign of negative inputs, making the function piecewise.

Explanation:

For

x < 0

|x| = -x

, so

f(x) = x(-x) = -x^2

Since

x \to -1

is a negative value, use the piece

-x^2

\displaystyle \lim_{x \to -1} f(x) = \lim_{x \to -1} (-x^2) = -(-1)^2 = -1

The limit is a single finite number.

Answer:

Option A:

-1

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