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