4.5 Newton’s Method

1-3. Compute , the third approximation to the root of the given equation using Newton's method with the specified initial approximation .

1.

2. .

3. .

4. Calculate the second approximation to the root of the equation by using Newton's method with initial approximation .

5-6. Approximate the given number using Newton's method.

5.

6.

7.

8.

9.

      (ⅰ)

      (ⅱ)

10.

      (ⅰ)

      (ⅱ)

11. Apply Newton's method to the equation to derive the following reciprocal algorithm:

    . Hence compute .

      (ⅰ)

12. Use Newton's method to find the absolute minimum value of the function .