The piecewise function is .

(a)

(i)

Find .

If  then the function .

.

(ii)

Find .

If  then the function .

.

If  then the function .

.

left hand limit and right hand limit are equal, so limit exist.

.

(iii)

Find .

If  then the function .

Substitute  in the above function.

.

(iv)

Find .

If  then the function .

.

(v)

Find .

If  then the function .

.

(vi)

Find .

.

.

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

 does not exist.

(b)

Graph :

Graph of the function is  :

(a) (i) .

     (ii) .

     (iii) .

     (iv) .

     (v) .

     (vi)  does not exist.

(b) Graph of the function is  is

.