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If L = l i m x → 0 e - x 2 2 - cos ⁡ x x 2 t a n 2 x , then the value of 3 L is equal to

Correct answer

0.25

Step-by-step solution

Using expansion series, we get, L = l i m x → 0 1 - x 2 2 + x 4 4 2 ! . . . - 1 - x 2 2 ! + x 4 4 ! - . . . x 2 x + x 3 3 + . . . 2 L = l i m x → 0 1 - 1 + - x 2 2 + x 2 2 + x 4 8 - x 4 24 + . . . . x 4 1 + x 2 3 + . . . . 2 ⇒ L = 1 8 - 1 24 = 1 12 Hence, 3 L = 0 . 25

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