Step 1:

The limit of the function is .

The squeeze theorem :

If when is near to ,  then .

Apply the squeeze theorem:

The range of cosine function is .

.

Multiply with throughout the equation.

By the squeeze theorem , and .

, then .

Therefore .

Solution:

.

(9)

Step 1:

The piecewise function is .

If , then .

If , then .

Find .

The left hand limit is .

.

Step 2:

The right hand limit is .

.

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

.

does not exist.

Step 3:

(10)

Find the limit is.

.

Solution:

(9) does not exist.

(10) .