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

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)


f(a) = 0 [from equation 2]

LHL = [ sin(–θ) = sinθ]

RHL = [from eqn 2]


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