Q24 of 155 Page 9

Prove that the function remains discontinuous at x = 0, regardless of the choice of k.

To prove given f(x) is discontinuous at x = 0, we have to show that left–hand limit(LHL) and right–hand limit(RHL) is unequal.


LHL = , since (c–h)<c


RHL = = , since (c + h)>c


LHL








–1


RHL








1


since


The function f(x)remains discontinuous at x = 0, regardless the choice of k.


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