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Paul
August 7, 2018

Calculus I - Assignment Problems
 Derivatives Previous Chapter Next Chapter Integrals Differentials Previous Section Next Section Business Applications

## Newton’s Method

For problems 1  3 use Newton’s Method to determine  for the given function and given value of .

1.

2. ,

3. ,

For problems 4  8 use Newton’s Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval.

4.  in

5.  in

6.  in

7.  in

8.  in

For problems 9  12 use Newton’s Method to find all the roots of the given equation accurate to six decimal places.

9.

10.

11.

12.

13. Suppose that we want to find the root to .  Is it possible to use  as the initial point?  What can you conclude about using Newton’s Method to approximate roots from this example?

14. Use the function  for this problem.

(a) Plot the function on the interval .

(b) Use  to find one of the roots of this function to six decimal places.  Did you get the root you expected to?

(c) Use  to find one of the roots of this function to six decimal places.  Did you get the root you expected to?

(d) Use  to find one of the roots of this function to six decimal places.  Did you get the root you expected to?

(e) What can you conclude about choosing values of  to find roots of equations using Newton’s Method.

15. Use  to find one of the roots of  accurate to six decimal places.  Did we chose a good value of  for this problem?

 Differentials Previous Section Next Section Business Applications Derivatives Previous Chapter Next Chapter Integrals

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