Discuss the continuity of the following functions at the indicated point(s).

at x = 0

In this problem we need to check continuity at x = 1

Given function is


at x = 0 …… Equation 2


we need to check LHL, RHL and value of function at x =0 (for approaching idea and meaning of continuity refer to Q10(i))


Clearly,


f(0) = 0 [ from equation 2]


LHL = [by putting x = –h in eqn 2]


=


RHL = [by putting x = h in eqn 2]


=


Clearly, LHL ≠ RHL ≠ f(0)


f(x) is discontinuous at x=0


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