help-CONTINUITY

Question

Answer 1

(5)

Step 1:

The function is on interval .

Intermediate value theorem:

If is continuous on the closed interval , , and is any number between and , then there is at least one number in such that .

In this case .

Find .

Substitute in .

.

Comments

Contd..

Step 2:

Find .

Substitute  in .

.

The function  is continuous on  with  and .

By Intermediate Value Theorem, there must be some  in such that .

The function  has a zero in the closed interval .

Solution:

The function  has a zero in the closed interval .

Answer 2

(6)

Step 1:

The function is on interval .

Intermediate Value Theorem:

If is continuous on the closed interval , , and is any number between and , then there is at least one number in such that .

In this case .

Find .

Substitute in .

.

Comments

Contd...

Step 2:

Find .

Substitute in .

.

The function is continuous on with and .

By Intermediate Value Theorem, there must be some in such that .

The function has a zero in the closed interval .

Solution:

The function has a zero in the closed interval .