Step 1:

(1)

The limit of the function is .

.

(2)

The limit of the function is .

.

(3)

The limit of the function is .

.

(4)

The limit of the function is .

Consider the function is .

Construct the table for different values of x near to 0.

Observe the table.

As x tends to 0 from left side, f(x) approaches to .

.

As x tends to 0 from right side, f(x) approaches to .

.

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

does not exist.

(5)

The limit of the function is .

.

(6)

The limit of the function is .

.

Solution :

(1) .

(2) .

(3) .

(4) does not exist.

(5) .

(6) .