Consider the function f x = sin ⁡ 2 x t a n 2 2 x ,   x ≠ π 4 . The value of f ( π 4 ) such that f is continuous at x = π 4 is

Step-by-step solution

f π 4   = lim x → π 4 ⁡ sin ⁡ 2 x tan 2 ⁡ 2 x = lim x → π 4 ⁡ e tan 2 ⁡ 2 x sin ⁡ 2 x - 1 =   lim x → π 4 ⁡ e sin ⁡ 2 x - 1 cot 2 ⁡ 2 x =   e lim x → π 4 2   cos   2 x   −   0 2   cot   2 x   ( − 2 cos e c 2   2 x ) = lim x → π 4     e − sin 3   2 x 2 = e − 1 2