help.

Question

Answer 1

(1)

The function is .

Find .

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

	3.5	3.9	3.99	3.999	3.9999
	112	14000	14x106	14x109	14x1012

Observe the table.

The value of at x = 3.9999 is 14x10¹².

As x tends to 4 from left side, approaches to large positive number.

Therefore .

Solution :

(1) .

Answer 2

(2)

The function is .

Find .

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

Observe the table.

The value of at x = 4.0001 is .

As x tends to 4 from right side, approaches to large negative number.

Therefore .

Solution :

(2) .

Answer 3

(3)

The function is .

Find .

Left hand limit :

As x tends to 4 from left side, approaches to large positive number.

.

Right hand limit :

As x tends to 4 from right side, approaches to large negative number.

.

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

does not exist.

Solution :

(3) does not exist.