JEE Main

JEE Main Mathematics question on Limits Continuity and Differentiability

lim⁡x→π4∫2sec⁡2xf(t) dtx2−π216\lim_{x \to \frac{\pi}{4}} \dfrac{\int_{2}^{\sec^2 x} f(t)\, dt}{x^2 - \dfrac{\pi^2}{16}} equals
  1. A.
    8πf(2)\dfrac{8}{\pi} f(2)
  2. B.
    2πf(2)\dfrac{2}{\pi} f(2)
  3. C.
    2πf ⁣(12)\dfrac{2}{\pi} f\!\left(\dfrac{1}{2}\right)
  4. D.
    4f(2)4f(2)
Show answer

Correct option: A

Previous-year question, JEE Main.

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