## 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.

- The left hand limit or right hand limit or both may not exist.
- The left hand limit or right hand limit exist but are not equal
- 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.

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

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