The document summarizes presentations from four students in the Ethernet Group on using the bisection method to find roots of equations. Student 1 presented on the bisection method algorithm. Student 2 used bisection method to find the root of x^3 - 2x - 3 = 0 to within 0.0001. Student 3 similarly used bisection method to find the root of x^3 - x - 2 = 0 to within 0.0001. Student 4 used bisection method to find the root of x^3 - 3x - 6 = 0 to within 0.0001, showing the iterative steps and calculations.

1. Numerical Methods
Presentation
Presentation Topic: Bisection Methods
Group Name: Ethernet

2. Ethernet Group
Md. Touhidur RahmanMd. Touhidur Rahman
Student ID: 152-15-6232Student ID: 152-15-6232

3. Algorithm of Bisection Method

4. Algorithm of Bisection Method

6. Proceeding this way the following table is required.

8. Ethernet Group
Sree Joyanto ChandroSree Joyanto Chandro
BarmonBarmon
Student ID: 152-15-6236Student ID: 152-15-6236

9. Using bisection method find the root of the equation X3
-2X-
3=0, where €=0.0001.

10. Proceeding this way the following table is required.
a b xr F(xr)
1 2 1.5 -2.625
1.5 2 1.75 -1.1406
1.75 2 1.875 -0.15820
1.875 2 1.9375 0.3982
1.875 1.9375 1.906 0.1121
1.875 1.906 1.8905 -0.0243
1.8905 1.906 1.8983 0.0440
1.8905 1.8983 1.8944 0.00973
1.8905 1.8944 1.8924 -0.00777
1.8924 1.8944 1.8934 0.00097
1.8924 1.8934 1.8930 0.00253

12. Ethernet Group
Hasan. Md. SadHasan. Md. Sad
AbdullahAbdullah
Student ID: 152-15-6235Student ID: 152-15-6235

13. Using bisection method. Find the root of the equation X3-X
-2 = 0 where = 0.0001ε

14. Proceeding this way the following table is required.
a b Xr F(Xr)
1 2 1.5 -
1.5 2 1.75 +
1.5 1.75 1.625 +
1.5 1.625 1.5625 +
1.5 1.5625 1.53125 +
1.5 1.53125 1.51562 -
1.51562 1.53135 1.52343 +
1.51562 1.52343 1.51953 -
1.51953 1.52343 1.52148 +
1.51953 1.52148 1.52050 -
1.52050 1.52148 1.52099 -
1.52099 1.52148 1.52124 -
1.52124 1.52148 1.52136 -

16. Ethernet Group
Tusher Chandro GhoshTusher Chandro Ghosh
Student ID: 152-15-6237Student ID: 152-15-6237

17. Using bisection method. Find the root of the equation X3-
3X - 6= 0 where = 0.0001ε

18. Proceeding this way the following table is required.
a b xr F(xr)
2 3 2.5 +
2 2.5 2.25 -
2.25 2.5 2.375 +
2.25 2.375 2.3125 -
2.3125 2.375 2.34375 -
2.34375 2.375 2.359375 +
2.34375 2.359375 2.3515625 -
2.3515625 2.359375 2.35546875 +
2.3515625 2.35546875 2.353515625 -
2.353515625 2.35546875 2.354492188 -
2.354492188 2.35546875 2.354980469 +

20. Thank YouThank You