For what value of k , the function defined by f ( x )   =   log ( 1 + 2 x ) sin x o x 2   for x ≠ 0 k for x = 0 is continuous at x = 0 ?

Step-by-step solution

Since f(x) is continuous at x = 0, hence lim x → 0 f ( x ) = f ( 0 ) ∴ lim x → 0 ⁡ log ⁡ 1 + 2 x . sin ⁡ x o x 2 = k ∴ lim x → 0 ⁡ 2 . log ⁡ 1 + 2 x 2 x ⋅ sin ⁡ x × π 180 x × π 180 × π 180 = k ⇒ 2 × π 180 = k ⇒ π 90 = k