Unit – IC

Removable and Non-removable Discontinuity

Reasons of Discontinuity:

The discontinuity of a function may be due to the following reasons (It is assumed the function f|(x) is defined at x = c.

  1. The left hand limit or right hand limit or both may not exist.
  2. The left hand limit or right hand limit exist but are not equal
  3. The left hand limit or right hand limit exist and are equal but not equal to f(c)

Removable Discontinuity:

A real valued function f(x) is said to have a removable discontinuity at x = c in its domain if

Thus the left hand and right hand limit of the function exist and they are equal. Thus the limit of function f(x) such that x → c exists, but this limit is not equal to the function value at x = c. Thus function is discontinuous at x = c. This type of discontinuity can be removed by redefining function f(x) at x = c such that



Non-removable Discontinuity:

A real valued function f(x) is said to have a non-removable discontinuity at x = c in its domain if

 Thus the left hand and right hand limit of the function exist and they are not equal. Thus the limit of function f(x) such that x → c does not exist. Thus function is discontinuous at x = c. By redefining the function this type of discontinuity can not be removed.

Non removable discontinuity is also referred as irremovable discontinuity.



Removable and non-removable Discontinuity

Filled circle indicates the function value i.e. f(c)

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