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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → 0 x 6 0 0 0 - sin x 6 0 0 0 x 2 sin x 6 0 0 0 is

Options

  1. A1000
  2. B100
  3. C1100
  4. D1010

Correct answer

A. 1000

Step-by-step solution

lim x → 0 ⁡ x 6000 - sin x 6000 x 2 sin x 6000 x 6000 . x 6000 0 0 lim x → 0 x 6 0 0 0 - sin x 6 0 0 0 x 6 0 0 2 = - lim x → 0 sin x 6 0 0 0 - x 6 0 0 0 x 6 0 0 2 = - lim x → 0 sin x x 6 0 0 0 - 1 x 2 = - lim x → 0 6 0 0 0 sin x x 5 9 9 9 x cos x - sin x x 2 2 x (By L-Hospital Rule) = - 6 0 0 0 2 lim x → 0 x cos x - sin x x 3 = - 3000   lim x → 0 cos x - x   sin x - cos x 3 x 2   = 1000

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