If the function f defined as f x = 1 x - k - 1 e 2 x - 1 , x ≠ 0 is continuous at x = 0 , then ordered pair k , f 0 is equal to

Step-by-step solution

Given f x = 1 x - k - 1 e 2 x - 1 ,   x ≠ 0 and f x is continuous at x = 0 . ⇒ f 0 = lim x → 0 1 x - k - 1 e 2 x - 1 = lim x → 0 1 + 2 x + 1 2 ! 2 x 2 + … - 1 - x k - 1 2 x 2 e 2 x - 1 2 x = lim x → 0 1 + 2 x + 1 2 ! 2 x 2 + … - 1 - x k - 1 2 x 2 Clearly, k = 3 and f 0 = 1 . ( ∵ Equating coefficient of x = 0 )