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

at x = 1

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

Given function is


at x = 1 …… Equation 2


we need to check LHL, RHL and value of function at x = 1 (for approaching idea and meaning of continuity refer to Q10(i))


Clearly,


f(1) = 2 [ from equation 2]


LHL =


Since h is positive no which is very close to 0


(h–2) is negative and hence h(h–2) is also negative.


|h(h–2)| = –h(h–2)


LHL =


RHL =


Since h is a positive no which is very close to 0


(h+2) is positive and hence h(h–2) is also positive.


|h(h+2)| = h(h+2)


RHL =


Clearly, LHL ≠ RHL


f(x) is discontinuous at x=1


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