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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Limits

NDA 2025 · Mathematics · Limits

For the following three (03) items: Consider the function f(x) =...

For the following three (03) items:
Consider the function f(x)=x∣x∣f(x) = x|x|.

What is lim⁡x→−1f(x)\lim_{x \to -1} f(x) equal to?

Options

  1. A−1-1
  2. B00
  3. C11
  4. DLimit does not exist

Correct answer

A. −1-1

Step-by-step solution

Given the function f(x)=x∣x∣f(x) = x|x|.

We need to evaluate lim⁡x→−1f(x)\lim_{x \to -1} f(x).

Since xx approaches −1-1, xx is negative, so ∣x∣=−x|x| = -x.

Thus, f(x)=x(−x)=−x2f(x) = x(-x) = -x^2 for x<0x < 0.

lim⁡x→−1f(x)=lim⁡x→−1(−x2)=−(−1)2=−1\lim_{x \to -1} f(x) = \lim_{x \to -1} (-x^2) = -(-1)^2 = -1.

Answer: −1-1
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