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GATE 2026 BT – Question 11

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 1 mark · Multiple choice

Consider the two functions $f_1(x) = \frac{x^2 - 4}{x - 2}$ and $f_2(x) = x^2 - 2x + 2$. Which of the following is the value of $(f_1(x) + f_2(x))$ as $x \to 2$?

  1. 0
  2. 6
  3. 8
  4. $\infty$

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Correct answer: (B) 6

Explanation

For $x \ne 2$, $f_1(x) = \frac{(x-2)(x+2)}{x - 2} = x + 2$, which tends to 4. At $x = 2$, $f_2 = 4 - 4 + 2 = 2$. The sum tends to $4 + 2 = 6$.