4.5   Newton’s Method                               by SGLee - HSKim - JHLee

                                                                                                             http://youtu.be/fdBHQ46g9RE

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 .

    http://matrix.skku.ac.kr/cal-lab/cal-Newton-method.html

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

5. 

    http://matrix.skku.ac.kr/2012-LAwithSage/interact/4/3.html 

      Let    .  Let  and find  by Newton's method with 

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 .

      Newton-Raphson Root Finding: http://matrix.skku.ac.kr/2012-LAwithSage/interact/4/3.html 

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