Answer :

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 = [ sin(–θ) = sinθ]


RHL = [from eqn 2]


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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