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JEE Main20209 Jan 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f x = s i n a + 2 x + s i n x x ; x < 0 b ; x = 0 x + 3 x 2 1 / 3 - x 1 / 3 x 1 / 3 ; x > 0 is continuous at x = 0 , then a + 2 b is equal to:

Options

  1. A1
  2. B- 1
  3. C0
  4. D- 2

Correct answer

C. 0

Step-by-step solution

f 0 - = lim x → 0 - sin a x cos 2 x x + sin 2 x cos a x x + sin x x = lim x → 0 - a cos 2 x + 2 cos a x + 1 = a + 3 Also, f 0 = b f 0 + = lim x → 0 x 1 3 x 1 3 1 + 3 x 1 3 - 1 x   , this is 0 0 form Apply LH Rule ⇒ f 0 + = 1 ∴   a = - 2 b = 1 ∴ a + 2 b = 0

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