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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