This document discusses several numerical methods for finding roots of equations, including the bisection method, false position method, fixed point method, Newton-Raphson method, and secant method. It provides an example of using the Newton-Raphson method to find the maximum deflection of a bookshelf beam. It also asks which function could be used with the fixed point method to find a root between 10 and 15 for the equation x3 - 30x2 + 2400 = 0. Finally, it provides an example of using the bisection method to find the root of the equation f(x)=3x+sinx-ex.

1. EXERCISES DUBAN CASTRO FLOREZ COD:2073091 METHODS TO CALCULATE ROOTS OF EQUATIONS

2. 1) If f(x)=e-x-xto find the root for the five methods. 0,56714329

3. BISECTION

4. FALSE POSITION

5. FIXED POINT

6. NEWTON-RAPHSON

7. SECANT

8. % Error # Iterations The methods that converges but express is Newton-Raphson and the method of the Secant.

9. 2) One plans to build a bookcase of books whose height is among 8½" and 11" with a longitude of 29". The bookcase is built in wood whose I Modulate of Young it is of 3.667Msi with a thickness of 3/8" and a width of 12". to Find the maximum vertical deflexión of the bookcase given for: Where x is the position along the beam. Therefore to find the maximum deflexión it is needed to know when and to make the derived test of second o'clock.

10. The equation that gives the position x where the deflexión is maximum it is given for: Use the method of Newton-Raphson to find the position x where the deflexión is maximum. Use three iterations to arrive to the root of the previous equation. Calculate the absolute relative error to the end of each iteration and the correct number of significant figures at the end of each iteration.

13. 3) It is wants to approach a root of the equation x3 - 30x2 + 2400 = 0 that we know are in the interval (10,15), by means of the method of the fixed point. Which of the following functions you would use to be able to wait convergence in the iteration process? Justify their answer.

15. 4) Si f(x)=3x+senx-exto calculate their root for the bisection method.

18. Presentations of teacher’s class(Eduardo Carrillo).

19. The graphs and the charts were you toss in the program Microsoft Excel.