Question

distinguish between essential holes and non essential holes ​

Answer 1

ANSWER

See the explanation below.

EXPLANATION

Geometrically, a removable discontinuity is a hole in the graph of f.

A non-removable discontinuity is any other kind of discontinuity. (Often jump or infinite discontinuities.)

Definition

If f has a discontinuity at a, but limx→af(x)exists, then f has a removable discontinuity at a 

("Infinite limits" are "limits" that do not exists.)

We remove the discontinuity by defining:

g(x)={f(x)ifx≠a and x∈domain(f)limx→af(x)ifx=a

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