The function f x = sin ⁡ x t a n 2 x is not defined at x = π 2 . The value of f π 2 such that f is continuous at x = π 2 is

Question

The function f x = sin ⁡ x t a n 2 x is not defined at x = π 2 . The value of f π 2 such that f is continuous at x = π 2 is, e, 1 e, 2, None of these

MARKS App · Accepted Answer

f is continuous at x = π 2 , if l i m x → π 2 f x = f π 2 Now, L = l i m x → π 2 sin ⁡ x t a n 2 x ⇒ log ⁡ L = l i m x → π 2 t a n 2 x log ⁡ sin ⁡ x = l i m x → π 2 log ⁡ sin ⁡ x c o t 2 x 0 0 = l i m x → π 2 c o t x 2 cot ⁡ x c o s e c 2 x = - 1 2 or L = e - 1 2 ∴ f π 2 = e - 1 2 = 1 e

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