NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of l i m x → 0 e - x 2 2 - cos ⁡ x x 3 tan ⁡ x is equal to

Options

A1 4
B1 8
C1 12
D1 16

Correct answer

C. 1 12

Step-by-step solution

Using expansion, l i m x → 0 1 + - x 2 2 + x 4 4 2 ! + . . . . - 1 - x 2 2 ! + x 2 4 ! - . . . . x 3 x + x 3 3 + . . . . l i m x → 0 1 - 1 + - x 2 2 + x 2 2 + x 4 8 - x 4 24 + . . . . x 3 x + x 3 3 + . . . . ⇒ 1 8 - 1 24 = 1 12

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