(5.00 Points) 4- For decreasing the number of iterations in Newton Raphson method a) b) C)...

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(5.00 Points) 4- For decreasing the number of iterations in Newton Raphson method a) b) C) d) e) The value of f" (x) must be increased The value of f" (x) must be decreased The value of f'(x) must be increased Xo must be used big value The value of f'(x) must be decreased Leave blank a) b) c) d) e) (5.00 Points) 5- According to table 1 values which one is the approximation of f1.7) (just degree 1, P(1.7)) by using Lagrange interpolation (You can find Lagrange polynomial formula below the table 1) Table 1 X 1.0 1.3 1.6 1.9 2.2 0.397541 0.1675144 0.7168271 0.5102968 0.2818186 Leave blank Useful formula for Lagrange Interpolation: P(x) = f(50)La,0(x) +---+ f(te)hax(8) = Σf(t)har(1), where, for each L... Lumi f(x) 0.7651977 0.6200860 0.4554022 0.2818186 0.1103623 (x-1)(x-3) D-A00-85 (2-4a80-17-14-400-4 -- Close (10.00 Points) 6- Find the most nearly value of fo2 reda by using the three-segment (n=3) trapezoidal rule. (general trapezoidal rule may be useful: f(x)da 4)) + f(0)]) 12.811 11.807 14.633 11.672 12.000 Leave blank n-1 b-a = f(a) + 2 (EH(a + ih) ) + 1 201 (10.00 Points) 7- Solve this system of equations and comment on the nature of the solution using the Gauss Elimination method. x+y+z=0 a) -z-y+3z=3 -#-y-z=2 Finite solutions Subzero solution) Unique Solution Infinitely many solutions No solution Leave blank 12. Ans (1.00 Points) 8- The function of f(x) is given by x²-4-0. If the initial value is xog-6, and the Newton Raphson method is performed what is the value of x₁ ? b) c) d) e) 713 f(x₁) f'(x) W 10/3 26/3 4/3 13/3 Leave blank Answ (10.00 Points) 9- Which one is the approximate solution of the fo zde by using Simpson's rule? (Simpson Formula may be useful: f(x)dx=f(ro) + 4f(2₁) + f(x₂)]) 8/3 4/3 20/3 4 Leave blank (5.00 Points) 10- The real value of a function f(x) which corresponds to the value of xo is 5. The result which is obtained by the polynomial approximation is 5.05. What is the percentage relative error of this approximation 2 e 0.5 0.01 -1 0.05 Leave blank (10.00 Points) 11- What will be the first iteration approximate solutions 21, 22, 23 of the following system of linear equations if we use Jacobi method? 5x12x2 + 3x3 = -1 - 3x1 +92 + 23 = 2 22122-723 = 3 a) (1.00,1.222,-0.425) (0.186,0.331,-0.423) (-0.200,0.156,-0.508) (-0.200,0.222,-0.429) (0.500,0.250,-0.200) Leave blank Ansv (5.00 Points) 12- Solve the given system of equation by the Gauss Elimination method. Select the correct option of x,y,z values. b) c) d) x+2y-z=-5 -2y+z=-4 4y - 3z = 2 (-2,1,1) (1,-1,1) (-9,5,6) (6,5,-9) (1,2,1) Leave blank. (3.00 Points) 13- Which one of the following is the value of r = for f(4) which is obtained from the Newton forward interpolation shown in the table? e e @ ixif(x) y 4 6 10 01 1 4 2 7 1.5 Leave blank 13 (5.00 Points) 15. The convergence of which of the following method is sensitive to starting value? a) b) d) e) False position Newton Raphson method All of these Gauss seidel method None of these Leave blank (1.00 Points) What is the Lagrange interpolation polynomial which passes through (1,5) and (2,2) a) b) c) d) e) P(x) = 3x+2 P(x)=-3x+8 P(x)= -x+6 P(x)= 3x-1 P(x)= x+2 Leave blank A (10.00 Points) 2- If we make an approximation to the value of f'(3) by using the second derivative formula (if h=1) according to the values of a function given, which of the following will be the result? (a) b) e co 0.25 4 i 0.5 1 Leave blank 02 13 2 4 Second derivative approximation formula: f" (ro)=f(ro-h)-25 (ro) + f (zo + h)] 5 8 12 Close (10.00 Points) 3- Which option we must use if we want to solve 23 from the following system of equation by using the Gauss-Siedel method? 521 + 2 + 3 = 2 2₁ +52 + 23 = 3 a) b) 21+523 + 24 = 5 2 + 3 + 524 = 2 (2-2₂-23) (3-21-23) (3-x2-x3) (5-71-7₁) (6-72-73) Leave blank (5.00 Points) 4- For decreasing the number of iterations in Newton Raphson method The value of f(x) must be increased- The value of f" (x) must be decreased The value of f'(x) must be increased Xo must be used big value The value of f'(x) must be decreased Leave blank (5.00 Points) 4- For decreasing the number of iterations in Newton Raphson method a) b) C) d) e) The value of f" (x) must be increased The value of f" (x) must be decreased The value of f'(x) must be increased Xo must be used big value The value of f'(x) must be decreased Leave blank a) b) c) d) e) (5.00 Points) 5- According to table 1 values which one is the approximation of f1.7) (just degree 1, P(1.7)) by using Lagrange interpolation (You can find Lagrange polynomial formula below the table 1) Table 1 X 1.0 1.3 1.6 1.9 2.2 0.397541 0.1675144 0.7168271 0.5102968 0.2818186 Leave blank Useful formula for Lagrange Interpolation: P(x) = f(50)La,0(x) +---+ f(te)hax(8) = Σf(t)har(1), where, for each L... Lumi f(x) 0.7651977 0.6200860 0.4554022 0.2818186 0.1103623 (x-1)(x-3) D-A00-85 (2-4a80-17-14-400-4 -- Close (10.00 Points) 6- Find the most nearly value of fo2 reda by using the three-segment (n=3) trapezoidal rule. (general trapezoidal rule may be useful: f(x)da 4)) + f(0)]) 12.811 11.807 14.633 11.672 12.000 Leave blank n-1 b-a = f(a) + 2 (EH(a + ih) ) + 1 201 (10.00 Points) 7- Solve this system of equations and comment on the nature of the solution using the Gauss Elimination method. x+y+z=0 a) -z-y+3z=3 -#-y-z=2 Finite solutions Subzero solution) Unique Solution Infinitely many solutions No solution Leave blank 12. Ans (1.00 Points) 8- The function of f(x) is given by x²-4-0. If the initial value is xog-6, and the Newton Raphson method is performed what is the value of x₁ ? b) c) d) e) 713 f(x₁) f'(x) W 10/3 26/3 4/3 13/3 Leave blank Answ (10.00 Points) 9- Which one is the approximate solution of the fo zde by using Simpson's rule? (Simpson Formula may be useful: f(x)dx=f(ro) + 4f(2₁) + f(x₂)]) 8/3 4/3 20/3 4 Leave blank (5.00 Points) 10- The real value of a function f(x) which corresponds to the value of xo is 5. The result which is obtained by the polynomial approximation is 5.05. What is the percentage relative error of this approximation 2 e 0.5 0.01 -1 0.05 Leave blank (10.00 Points) 11- What will be the first iteration approximate solutions 21, 22, 23 of the following system of linear equations if we use Jacobi method? 5x12x2 + 3x3 = -1 - 3x1 +92 + 23 = 2 22122-723 = 3 a) (1.00,1.222,-0.425) (0.186,0.331,-0.423) (-0.200,0.156,-0.508) (-0.200,0.222,-0.429) (0.500,0.250,-0.200) Leave blank Ansv (5.00 Points) 12- Solve the given system of equation by the Gauss Elimination method. Select the correct option of x,y,z values. b) c) d) x+2y-z=-5 -2y+z=-4 4y - 3z = 2 (-2,1,1) (1,-1,1) (-9,5,6) (6,5,-9) (1,2,1) Leave blank. (3.00 Points) 13- Which one of the following is the value of r = for f(4) which is obtained from the Newton forward interpolation shown in the table? e e @ ixif(x) y 4 6 10 01 1 4 2 7 1.5 Leave blank 13 (5.00 Points) 15. The convergence of which of the following method is sensitive to starting value? a) b) d) e) False position Newton Raphson method All of these Gauss seidel method None of these Leave blank (1.00 Points) What is the Lagrange interpolation polynomial which passes through (1,5) and (2,2) a) b) c) d) e) P(x) = 3x+2 P(x)=-3x+8 P(x)= -x+6 P(x)= 3x-1 P(x)= x+2 Leave blank A (10.00 Points) 2- If we make an approximation to the value of f'(3) by using the second derivative formula (if h=1) according to the values of a function given, which of the following will be the result? (a) b) e co 0.25 4 i 0.5 1 Leave blank 02 13 2 4 Second derivative approximation formula: f" (ro)=f(ro-h)-25 (ro) + f (zo + h)] 5 8 12 Close (10.00 Points) 3- Which option we must use if we want to solve 23 from the following system of equation by using the Gauss-Siedel method? 521 + 2 + 3 = 2 2₁ +52 + 23 = 3 a) b) 21+523 + 24 = 5 2 + 3 + 524 = 2 (2-2₂-23) (3-21-23) (3-x2-x3) (5-71-7₁) (6-72-73) Leave blank (5.00 Points) 4- For decreasing the number of iterations in Newton Raphson method The value of f(x) must be increased- The value of f" (x) must be decreased The value of f'(x) must be increased Xo must be used big value The value of f'(x) must be decreased Leave blank

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The detailed answer for the above question is provided below Answer 4 option e is correct For dec... View the full answer