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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → 0 ⁡ cos ⁡ x + sin ⁡ b x a x is equal to

Options

  1. Ae - a b
  2. Be a b 2
  3. Ce a b
  4. De - b 2 a

Correct answer

C. e a b

Step-by-step solution

Let, L = lim x → 0 ⁡ cos ⁡ x + sin ⁡ b x a x = e lim x → 0 ⁡ a x cos ⁡ x + sin ⁡ b x - 1 (using 1 ∞ form) L = e lim x → 0 ⁡ a - sin ⁡ x + b cos ⁡ b x 1 = e a b

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