Q9 of 48 Page 358

Show that ƒ(x) = is continuous at each point except 0.

Given function is ƒ(x) =


Left hand limit at x = 0


= 0


Right hand limit at x = 0


= 0


Also,


f(0) = 1


As,



f(x) = x for other values of x expect 0 f(x) = 1,2,3,4…


Therefore,


f(x) is not continuous everywhere expect at x = 0


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