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))
f(1) = 2 [ from equation 2]
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)
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