C3 Mei - Numerical Methods to solve equations

... C3 Coursework In this coursework, I will use numerical methods to solve the following equation, as I cannot solve it algebraically. I can only obtain an approximation of the solution as it is impossible or hard to find the exact value of the function. Decimal Search The graph below is the function I will use decimal search in order to find an approximation of one of the roots. The table below shows decimal search. Each boundary is tested for sign change which indicates that a root exists between them. The x where the sign change occurs in now the new boundaries and tested for sign change again. This method is repeated until an approximation of the root is found to a suitable number of decimal places. x f(x) 0 2 0.1 1.9501 0.2 1.8016 0.3 1.5581 0.4 1.2256 0.5 0.8125 0.6 0.3296 0.7 -0.2099 0.8 -0.7904 0.9 -1.3939 1 -2 x f(x) 0.66 0.011747 0.661 0.006295 0.662 0.000838 0.663 -0.00462 0.664 -0.01009 0.665 -0.01556 0.666 -0.02104 0.667 -0.02652 0.668 -0.032 0.669 -0.03749 0.67 -0.04299 x f(x) 0.662 0.000838 0.6621 0.000292 0.6622 -0.00025 0.6623 -0.0008 0.6624 -0.00135 0.6625 -0.00189 0.6626 -0.00244 0.6627 -0.00299 0.6628 -0.00353 0.6629 -0.00408 0.663 -0.00462 x f(x) 0.6 0.3296 0.61 0.277958 0.62 0.225763 0.63 0.17303 0.64 0.119772 0.65 0.066006 0.66 0.011747 0.67 -0.04299 0.68 -0.09819 0.69 -0.15383 0.7 -0.2099 [0, 1] [0.6, 0.7] [0.66, 0.67] [0.662, 0.663] Root intervals [0.6621, 0.6622] I know that the root is 0.662 to 3 decimal places In order to

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