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JEE Main202127 Jul 2021Evening ShiftMathematicsLimitsActual

The value of lim x → 0 x 1 - sin x 8 - 1 + sin x 8 is equal to :

Options

  1. A0
  2. B4
  3. C- 4
  4. D- 1

Correct answer

C. - 4

Step-by-step solution

lim x → 0 x 1 - sin x 8 - 1 + sin x 8 = lim x → 0 x 1 - sin x 8 - 1 + sin x 8 × 1 - sin x 8 + 1 + sin x 8 1 - sin x 8 + 1 + sin x 8 × 1 - sin x 4 + 1 + sin x 4 1 - sin x 4 + 1 + sin x 4 × 1 - sin x + 1 + sin x 1 - sin x + 1 + sin x = lim x → 0 x 1 - sin x - ( 1 + sin x ) × 1 - sin x 8 + 1 + sin x 8 1 - sin x 4 + 1 + sin x 4 1 - sin x + 1 + sin x = lim x → 0 x ( - 2 sin x ) 1 - sin x 8 + 1 + sin x 8 × 1 - sin x 4 + 1 + sin x 4 1 - sin x + 1 + sin x = lim x → 0 -

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