If the function f ( x ) defined by f x = x sin ⁡ 1 x f o r x ≠ 0 k f o r x = 0 is continuous at x = 0 , then k = _______

Step-by-step solution

f x = x sin ⁡ 1 x f o r x ≠ 0 k f o r x = 0 Since f ( x ) is continuous at x = 0 ⇒ lim x → 0 f ( x ) = f ( 0 ) ∴ lim x → 0 ⁡ x sin ⁡ 1 x = k ⇒ 0 = k ( ∵ sin ( 1 x ) ∈ [ − 1 , 1 ] f o r a l l x ≠ 0 )