Q10 of 26 Page 1

Show that the function f given by :

is discontinuous at


The function f will be discontinuous at x = a in any of following cases :


(i) and exist but are not equal.


(ii) and exist and are equal but not equal to f (a).


(iii) f (a) is not defined.


Now, we check the Left-hand limit of f at x = 0



Similarly, right-hand limit of f at x = 0




Thus,


Hence, f is discontinuous at x = 0


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