1. Compute integral Je-* dx using composite trapezoidal rule with 5 integration points. Estimate the integration error. (4 grading points) 3. Find the root of the equation e * - sin(x) cos (x) = 0 using Newton-Raphson algorithm. Perform three iterations from the starting point X, = 0. (3 grading points). Estimate the error. (1 grading point). 5. Compute the first derivative of the function f (x) = x3 - 3x + 1 at the point Xo = 6 using 5 point formula with / = 2. (3 grading points). What is the differentiation error? (1 grading point). 7. Suppose, we need to differentiate numerically the following function f(x) = -10x2 - 1.3x + 1 Which differentiation rule (forward, backward, 3 point, or 5 point) would the most efficient to use in terms of computational performance and accuracy? Please explain. (3 grading points) 8. Obtain numerical solution of the ordinary differential equation y' = 3t - 4y with boundary condition: y(0) = 4 by Euler method using h = 0.5 Perform 3 steps. (4 grading points) Solution of all problems MUST contain general formula and all intermediate results. Perform numerical computations using 4 significant digits