Page 1 :
a “Su 7:48 @ MBS Kare, , € stdtimathpa.. El] QQ:, , 8.1.2 DEFINITION OF CONTINUITY, , A function /(x) is said to be continuous at a point, x =a, if the following three conditions are, satisfied:, , i. fis defined at every point on an open interval, containing a., , il. lim f(x) exists, x>a, , , , , , iii, lim f(x) =f(@)., , Among the three graphs given above, decide, which conditions of continuity are not satisfied., , The condition (iii) can be reformulated and the, continuity of f(x) at x = a, can be restated as, follows :, , A function f(x) is said to be continuous, at a point x = a if it is defined in some, , neighborhood of ‘a’ and if, , lim [f(a +h) -f@] =0., , , , G, , Illustration 1. Let f(x) = |x| be defined o.._., , = C a)