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.

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:

.

(3)

Step 1:

The limit expression is .

Factorize the denominator.

Cancel common terms.

.

.

Solution:

.

(4)

Step 1:

The limit expression is .

.

.

Solution:

.

(7)

Step 1:

The limit expression is .

Verify the limit by using table. \ \

A limit in which increases or decreases without bound as approaches is called an infinite limit.

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, then the limit does not exist. \ \

does not exist. \ \

Solution:

does not exist. \ \

\ \

\ \

\ \

\ \

.

Solution:

.

(5)

Step 1:

The limit expression is .

Cancel common terms.

As , then .

\ \

.

.

Solution:

.

(6)

Step 1:

The limit expression is .

Factorize the numerator and denominator.

Cancel the common terms.

.

.

Solution:

.

(7)

Step 1:

The limit expression is .

Factorize the numerator and denominator.

Cancel the common terms.

.

.

Solution:

.

(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.

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:

.