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JEE Main2015MathematicsLimitsActual

lim x → 0 ⁡ e x 2 - cos ⁡ x sin 2 ⁡ x is equal to

Options

  1. A2
  2. B3 2
  3. C5 4
  4. D3

Correct answer

B. 3 2

Step-by-step solution

lim x → 0 e x 2 - cos x sin 2 x = lim x → 0 ( e x 2 − 1 ) + ( 1 − cos x ) x 2 · sin 2 x x 2 = lim x → 0 e x 2 − 1 x 2 + 1 − cos x x 2 = 1 + 1 2 = 3 2

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