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JEE Main20205 Sep 2020Morning ShiftMathematicsLimitsActual

If α is the positive root of the equation, p x = x 2 − x − 2 = 0 , then lim x → α + 1 − cos p x x + α − 4 is equal to

Options

  1. A3 2
  2. B3 2
  3. C1 2
  4. D1 2

Correct answer

B. 3 2

Step-by-step solution

Given, p x = 0 ⇒ x 2 - x - 2 = 0 ⇒ x - 2 x + 1 = 0 ⇒ x = 2 , - 1    ∴    α = 2 Now, lim x → 2 + 1 − cos x 2 − x − 2 x − 2 = lim x → 2 + 2 sin 2 x 2 − x − 2 2 x − 2 = lim x → 2 + 2 · sin x 2 - x - 2 2 x - 2 = lim x → 2 + 2 · sin x 2 - x - 2 2 x - 2 (because x > 2 ) = lim x → 2 +   2 sin x 2 - x - 2 2 x 2 - x - 2 2 · 2 · x 2 - x - 2 x - 2 = lim x → 2 + 1 2 ·

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