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

at x = a

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

Given function is

at x = a …… Equation 2

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

Clearly,

f(a) = 0 [from equation 2]

LHL = [putting x = (a–h) in eqn 2]

=

RHL =

=

Why

Since whatever is value of h, sin(1/h) is going to range from –1 to 1

As h→ 0 ,i.e. approximately 0

∴ 0*some finite quantity is equal to 0.

Clearly, LHL = RHL = f(a)

∴ f(x) is continuous at x = 0

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