21. The accuracy of Simpson's rule quadrature for a step size h is
22. The table below gives values of a function F(x) obtained for values of x at intervals of 0.25.
x
0
0.25
0.5
0.75
1.0
F(x)
1
0.9412
0.8
0.64
0.50
The value of the integral of the function between the limits 0 to 1 using Simpson's rule is
| x | 0 | 0.25 | 0.5 | 0.75 | 1.0 |
| F(x) | 1 | 0.9412 | 0.8 | 0.64 | 0.50 |
The value of the integral of the function between the limits 0 to 1 using Simpson's rule is
23. A numerical solution of the equation f(x) = x + √x - 3 = 0 can be obtained using Newton-Raphson method. If the starting value is x = 2 for the iteration, the value of X that is to be used in the next step is
24. To solve the equation 2sin x = x, by Newton Raphson method, the initial guess value is chosen to be x = 2. Consider x in radius only. The value of x (in radius) obtained after one iteration will be closed to
25. A 2nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $$\int\limits_0^2 {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$ is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as "true value - approximate value") in the estimate?
26. Starting from x0 = 1, one step of Newton-Raphson method in solving the equation x3 + 3x - 7 = 0 gives the next value (x1) as
27. The equation x3 - x2 + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then the next approximation using this method will be
28. The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson's method is
29. Equation ex - 1 = 0 is required to be solved using Newton's method with an initial guess x0 = -1. Then, after one step of Newton's method, estimate x1 of the solution will be given by
30. Match List-I with List-II and select the correct answer:
List-I
List-II
a. Newton-Raphson method
1. Solving nonlinear equations
b. Runge-Kutta method equations
2. Solving simultaneous linear equations
c. Simpson's Rule equations
3. Solving ordinary differential
d. Gauss elimination
4. Numerical integration
5. Interpolation
6. Calculation of Eigenvalues
| List-I | List-II |
| a. Newton-Raphson method | 1. Solving nonlinear equations |
| b. Runge-Kutta method equations | 2. Solving simultaneous linear equations |
| c. Simpson's Rule equations | 3. Solving ordinary differential |
| d. Gauss elimination | 4. Numerical integration |
| 5. Interpolation | |
| 6. Calculation of Eigenvalues |