NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of l i m x → 0 e x - x - 1 x - sin ⁡ x l n 1 + x x 6 is equal to

Options

A1 2
B1 6
C1 12
D1 3

Correct answer

C. 1 12

Step-by-step solution

Let, L = l i m x → 0 e x - x - 1 x 2 x - sin ⁡ x x 3 ln ⁡ 1 + x x Applying expansion series, we get, L = l i m x → 0 1 + x + x 2 2 ! … . - x + 1 x - x - x 3 3 ! + x - x 2 2 + … x 6 = 1 2 . 1 6 . 1 = 1 12

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