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(Solved): 12- Use the gauss-Seidel method to find the approximate solution of the syste ...
12- Use the gauss-Seidel method to find the approximate solution of the system to within a tolerance of \( 0.01 \) \[ \begin{array}{c} 10 \mathrm{x}_{1}-\mathrm{x}_{2}=9 \\ -\mathrm{x}_{1}+10 \mathrm{x}_{2}-2 \mathrm{x}_{3}=7 \\ -2 \mathrm{x}_{2}+10 \mathrm{x}_{3}=6 \end{array} \] 13- Use NFDF to obtain the highest possible interpolating polynomial representing the following data, then find the approximate value of \( f(1.5) \) 14- Use two and three points formulas to approximate numerical differential \( \mathbf{f}^{\prime}(\mathbf{4}) \) if \( f(x) \) is given by the function \( f(x)=x^{3} e^{x}+2 x \) with \( \mathrm{h}=0.1 \)
Expert Answer
Two points formula: Let x0 = 4 and h = 0.1 Then, f(x0) = f(4) = (4^3)(e^4) + 2(4) = 748.935 and f(x0+h) = f(4.1) = (4.1^3)(e^4.1) + 2(4.1) = 809.611 T