Answer to Question #69038 in Real Analysis for devangi

Question

Check whether the following functions are continuous or not at x = 0. Also, find
the nature of discontinuity at that point, if it exists.
(i) f(x)= {[(2-x)^(1/2) - (2+x)^(1/2)] / [x] , x≠0 ; 1/√2 , x=0
(ii) f(x)= { x^(2)+1/3, x≤0 ; -[x^(3)+1/3], x>0