Step 1:

The function is .

(1)

Find .

The function is .

Construct the table for different values of x near to 4 from left :

Observe the table.

The value of f(x) at x = 3.9999 is 14x10¹².

As x tends to 4 from left side f(x) approaches to large positive number.

Therefore .

Step 2:

(2)

Find .

The function is .

Construct the table for different values of x near to 4 from right :

Observe the table.

The value of f(x) at x = 4.0001 is .

As x tends to 4 from right side f(x) approaches to large negative number.

Therefore .

Step 3:

(3)

Find .

The function is .

Left hand limit :

As x tends to 4 from left side f(x) approaches to large positive number.

.

Right hand limit :

As x tends to 4 from right side f(x) approaches to large negative number.

.

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

does not exist.

Solution :

(1) .

(2) .

(3) does not exist.