The Newton-Raphson method is used to find the root of a function by iteratively guessing values that get closer to the root. It involves writing the function, taking its derivative, and using the previous guess to calculate the next guess until the guesses converge on the root. The document provides examples of using Newton-Raphson as well as the fixed point and secant methods, which similarly find roots through iterative guessing.

1. Newton-RaphsonMethod© carlosduranmethods.blogspot.com

2. The Newton-Raphson method can be used for finding the root of some functions. © carlosduranmethods.blogspot.com

3. These are thestepsStep 1: WriteoutStep 2: Find , thederivative of Step 3: FindStep 4: RepeatStep 3, until© carlosduranmethods.blogspot.com

4. The best way to explain this is through an example.Example: find the roots to the following equationArbitrarily pick a number, I choose 1to start© carlosduranmethods.blogspot.com

5. In this case, therootisbetween 1,92035677 and 1,92017514© carlosduranmethods.blogspot.com

6. FixedpointMethod© carlosduranmethods.blogspot.com

7. The aim of this method is to find a value of xthenfind a value of xOntheotherhand, you can find all the ways to clear the x, and try with some.Again, I´mgointoexplainyouthroughanexample.© carlosduranmethods.blogspot.com

8. FindtherootfromthenextfunctionI start the iterations with© carlosduranmethods.blogspot.com

9. © carlosduranmethods.blogspot.com

10. SecantMethod© carlosduranmethods.blogspot.com

11. The application of this method is the same as the previous ones, but the value of x changes.in general terms the formula is:the term n-2 is included in the formula, this implies that we take two values.© carlosduranmethods.blogspot.com

12. Findtheroot, forthenextfunctionWith and © carlosduranmethods.blogspot.com

13. Finally, the number of iterations foreachmethoddepends on tolerance© carlosduranmethods.blogspot.com