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JEE Main20198 Apr 2019Morning ShiftMathematicsLimitsActual

l i m x → 0 s i n 2 x 2 - 1 + c o s x equals

Options

  1. A4 2
  2. B2 2
  3. C2
  4. D4

Correct answer

A. 4 2

Step-by-step solution

l i m x → 0   s i n 2 x 2 - 1 + c o s x On Rationalisation, we get, = l i m x → 0   s i n 2 x 2 - 1 + c o s x × 2 + 1 + c o sx 2 + 1 + c o sx = l i m x → 0   2 sin x 2 cos x 2 2 1 - c o s x × 2 + 1 + cos x = l i m x → 0   4 s i n 2 x 2 c o s 2 x 2 2 s i n 2 x 2 × 2 + 1 + cos x = l i m x → 0   2 c o s 2 x 2 2 + 1 + c o s x = 2 × 2 2 = 4 2 .

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