Now let a be any arbitrary element of R then there arise two cases Case I If a 0 then and 1 lim f x lim x sin X NI 2 M X Now f a asin 1 asin 1 a whenever Continuity of Functions a Then lim f x f a a sin X M SITY I Q 2 I Q 3 1 Thus f x is continuous at x a Case II If a 0 then by the definition of function f a f 0 0 a x 0 xsin 0 si S A Sin JO f x f 0 Now if we choose s then for a given 0 there exists a number 8 E 0 such that That f x f 0 e x 0 x 8 Thus f x is continuous at x 0 Hence f x is continuous on R OF DEL Institute of Lifelong Learning University of Delhi Continuity of Functions pg 8 8