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GATE 2025 BT – Question 46

Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 2 marks · Multiple choice

If the function $f(x) = \begin{cases}\sin 2x, & x > 0 \\ a + bx, & x \le 0\end{cases}$ where $a$ and $b$ are constants, is differentiable at $x = 0$, then $a + b$ is equal to

  1. 0
  2. 1
  3. 2
  4. 3

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Correct answer: (C) 2

Explanation

Continuity at 0 requires $a = \sin 0 = 0$. The derivative from the right is $2\cos 0 = 2$ and from the left it is $b$, so $b = 2$. Then $a + b = 2$.