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# Exercise roots of equations

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### Exercise roots of equations

1. 1. EXERCISES<br />DUBAN CASTRO FLOREZ<br />COD:2073091<br />METHODS TO CALCULATE ROOTS OF EQUATIONS<br />
2. 2. 1) If f(x)=e-x-xto find the root for the five methods.<br />0,56714329<br />
3. 3. BISECTION<br />
4. 4. FALSE POSITION<br />
5. 5. FIXED POINT<br />
6. 6. NEWTON-RAPHSON<br />
7. 7. SECANT<br />
8. 8. % Error<br /># Iterations<br />The methods that converges but express is Newton-Raphson and the method of the Secant.<br />
9. 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: <br /> <br /> <br />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.<br />
10. 10. The equation that gives the position x where the deflexión is maximum it is given for: <br />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. <br />
11. 11.
12. 12.
13. 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.<br />
14. 14.
15. 15. 4) Si f(x)=3x+senx-exto calculate their root for the bisection method.<br />
16. 16.
17. 17. BIBLIOGRAPHY<br /><ul><li>CHAPRA, Steven C. y CANALE, Raymond P.: Numérics Méthods for Engineers. McGraw Hill 2002.
18. 18. Presentations of teacher’s class(Eduardo Carrillo).
19. 19. The graphs and the charts were you toss in the program Microsoft Excel.</li>