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Step-by-step Answer
PAGE: 93SET: ExercisesPROBLEM: 43
Please look in your text book for this problem Statement

The function is .

The function  is continuous over the interval  and .

Check the continuity of the function at .

Definition of continuity :

A function  is continuous at , if  then it should satisfy three conditions :

(1)  is defined.

(2)  exists.

(3) .

Check the continuity of the function at .

Condition (1):

 is defined.

If  then the function is .

.

Condition (2):

 exists.

Left hand limit :

Right hand limit :

Left hand limit and right hand limit are not equal, limit does not exist.

 does not exist.

The limit does not exist at .

Therefore the function  is discontinuous at .

 and .

.

Therefore the function  is continuous at  from right side.

Check the continuity of the function at .

Condition (1):

 is defined.

If  then the function is .

.

Condition (2):

 exists.

Left hand limit :

Right hand limit :

Left hand limit and right hand limit are not equal, limit does not exist.

 does not exist.

The limit does not exist at .

Therefore the function  is discontinuous at .

 and .

.

Therefore the function  is continuous at  from left side. 

Graph :

Graph the function  :

The function  is discontinuous at  and it is continuous from right side.

The function  is discontinuous at  and it is continuous from left side.

Graph of the function  is

.



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