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GATE 2025 AE – Question 15

Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 1 mark · Multiple choice

$f(x) = \begin{cases} A + x, & x < 2 \\ 1 + x^2, & x \ge 2 \end{cases}$

If the function $f(x)$ is continuous at $x = 2$, the value of $A$ is _____.

  1. 2
  2. 2.5
  3. 3
  4. 3.5

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Correct answer: (C) 3

Explanation

Continuity at $x = 2$ needs the two pieces to agree there: $A + 2 = 1 + 4 = 5$, so $A = 3$.