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JEE Main201910 Apr 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f x = s i n ( p + 1 ) x + s i n x x , x < 0 q , x = 0 x + x 2 - x x 3 / 2 , x > 0 is continuous at x = 0 , then the ordered pair ( p , q ) is equal to:

Options

  1. A- 3 2 , - 1 2
  2. B- 1 2 , 3 2
  3. C5 2 , 1 2
  4. D- 3 2 , 1 2

Correct answer

D. - 3 2 , 1 2

Step-by-step solution

∵       f x = sin ⁡ p + 1 x   + s i n x x q x 2 + x - x x 3 / 2     : x < 0 : x = 0 : x > 0   ∵ f is continuous at x = 0 L . H . L = l i m h → 0   sin p + 1 - h + s i n ( - h ) - h = l i m h → 0 sin p + 1 h + sin h h = l i m h → 0 sin p + 1 h h p + 1 p + 1 + lim h → 0 sin h h = p + 1 + 1 = p + 2 R . H . L =   l i m h → 0   h 2 + h -   h h 3 2 ×   h 2 + h + h h 2 + h + h = l i m h → 0 h 2 +

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