If f x = 2 x - 1 2 tan ⁡ 3 x x s i n 2 x λ : : 0 < x < π 6 x = 0 is continuous at x = 0 , then the value of 10 3 λ l n 2 is equal to

Step-by-step solution

∵   f x is continuous at x = 0 ∴   l i m x → 0 f x = f 0 ∵ l i m x → 0 + 2 x - 1 2 tan ⁡ 3 x x . s i n 2 x = λ ∵ l i m x → 0 + 2 x - 1 x 2 tan ⁡ 3 x 3 x . 3 x x x 2 s i n 2 x = λ ln ⁡ 2 2 . 1.3 . 1 = λ 10 3 λ ln ⁡ 2 = 30