limits

Question

Answer 1

Step 1:

1)The limit value is .

If .

Step 2:

2)

The limit is .

           (Since )

Recall property of limit:.

Answer 2

Continued:

Step 3:

3)

The limit function is .

Recall property of limit:.

Step 4:

4)

The limit function is

Find the left hand limit :

           (Since )

Find the right hand limit:

               (Since )

Since the left hand limit is not equal to the right hand limit, limit does not exist.

Limit does not exist at .

Solution:

1) .

2) .

3) .

 

4) Limit does not exist at .

Answer 3

Step 1:

5)The limit value is .

Consider .

Multiply the numerator and denominator by .

                            (Since )

 

substitute in.

.

 

Solution:

5).

Answer 4

Step 1:

6)The limit is

                      (Since )

.

 

Solution:

6).