help plz.

Question

Answer 1

(11)

Step 1:

The limit of the function is .

Squeeze theorem :

If when is near to , then .

The range of cosine function is .

Multiply with throughout the equation.

By the squeeze theorem , and .

, then .

Therefore .

Solution:

.

Answer 2

(9)

Step 1:

The piecewise function is .

If , then .

If , then .

Limit Definition:

if and only if and .

Step 2:

Find .

The left hand limit is .

.

Step 3:

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.

Solution:

does not exist.

Answer 3

(10)

Step 1:

The piecewise function is .

If , then .

If , then .

Find the limit .

.

Solution:

.