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