If the function f x = sin ⁡ 3 x + a sin ⁡ 2 x + b x 3 ,   x ≠ 0 is continuous at x = 0 and f 0 = K ,   ∀ K ∈ R , then b - a is equal to

Step-by-step solution

∵ f x is continuous at x = 0 ∴ lim x → 0 ⁡ f x = f 0 = f i n i t e lim x → 0 ⁡ sin ⁡ 3 x + a sin ⁡ 2 x + b x 3 = f i n i t e For lim x → 0 ⁡ 3 x - 27 x 3 3 ! + … + a 2 x - 8 x 3 3 ! + … + b x 3 to be finite b = 0 , 3 + 2 a = 0 So, a = - 3 2