Prove that the function remains discontinuous at x = 0, regardless of the choice of k.

Question

Philoid · Accepted Answer

To prove given f(x) is discontinuous at x = 0, we have to show that left–hand limit(LHL) and right–hand limit(RHL) is unequal.

LHL = , since (c–h)

RHL = = , since (c + h)>c

LHL

–1

RHL

1

since

The function f(x)remains discontinuous at x = 0, regardless the choice of k.