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  3. 1 consider the equationx sin x l prove the equation...

Question: 1 consider the equationx sin x l prove the equation...

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1. Consider the equationx sin x L Prove the equation has one and one root 1o.1 L Construct a fised-point iterative scheme and Newtoms method to find the approximation Xg with the initial value Xo 05, respectively Compare th, result in the question and discuss ther convergence. L Use the Lagrange interpolating polymomial with degree 2 to find an L Estimate the error (o.5)- (0.5) Find the approximation using trapezoid rule. 4. Consider the linear system +2x2 x3-12 -x, +4x2 + 2x3 = 20 2x-3x2+10x-3 L Construct the Jacobi; Gausis-seided and Soit nerative scheme for solving the IL Test the convergence of the lacobi and Gauss-seided method L If the jacobi method is convergent, estimate the number of iterations necessary with tolerance E-10for an initial vector -(00p) 5. Use Gaussian elimination method and Gaussian elimination method with partial pivoting to solive the following linear system with 4-digit rounding aichmetic 0.00122 1x1 +x2 = 1 6. Consider the matrix A 99 0.9 Find Cond, (A), Cond2 (B) and p(B). 7. Suppose x 3.141 is an approximation of 3.1415926 Find the number of significant digits, absolute error bound and relative error bound of x
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