help.? lc

Question

Answer 1

(2)

Step 1:

The limit expression is .

When  tends to  from the right side, is a small positive number.

Thus, the quotient  is a large positive number and  approaches infinity from the right of .

.

 increases without bound as approaches  from the right.

Comments

Contd...

Verify the limit by using the table.

As limit in which  increases without bound as approaches  from the right is called as an infinite limit.

Therefore, .

Solution:

.

Answer 2

(3)

Step 1:

The limit expression is .

Factorize the denominator.

Cancel common terms.

.

.

Solution:

.

Answer 3

(4)

Step 1:

The limit expression is .

.

.

Solution:

.

Answer 4

(5)

Step 1:

The limit expression is .

Cancel common terms.

As , then .

.

.

Solution:

.

Answer 5

(6)

Step 1:

The limit expression is .

Factorize the numerator and denominator.

Cancel the common terms.

.

.

Solution:

.

Answer 6

(7)

Step 1:

The limit expression is .

Construct a table for different values of .

 

Comments

Contd...

Observe the table:

As tends to from the left hand side, approaches .

 .

As tends to from the right hand side, approaches .

.

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

does not exist.

Solution:

does not exist.