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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of l i m x → 0 sec ⁡ x + tan ⁡ x 1 x is equal to

Options

  1. Ae
  2. Be 2
  3. Ce - 1
  4. D1

Correct answer

A. e

Step-by-step solution

l i m x → 0 sec ⁡ x + tan ⁡ x 1 x ( 1 ∞ form) = e l i m x → 0 1 x sec ⁡ x + tan ⁡ x - 1 = e l i m x → 0 1 + sin ⁡ x - cos ⁡ x x cos ⁡ x = e l i m x → 0 cos ⁡ x + sin ⁡ x - x sin ⁡ x + cos ⁡ x   b y   L ' H o s p i t a l   rule = e 1 + 0 0 + 1 = e

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