Question

Q1/ Find the interpolation or extrapolation of the following data by using 1) Lagrange formula 2) Gregory-Newton formula 3) Newton's divided difference formula 4) The method of least square of second order x | -1.5 | 0 | 1.5 | 3 | 4 | 5.5 | 7 | 9 f(x) | -10 | -7 | -0.5 | 8 | 25 | 32 | 44 | 51 Q2/ Find the numerical differentiation of the value x = 0, and x = 4 for the data in (Q1) as follows: 1) Second derivative when using five pointes, two points before point (i) and two points after point (i). 2) Fourth derivative when using five pointes, two points before point (i) and two points after point (i). Q3/ Find the numerical integration of equation y = xlnx^2 - ^2sqrt{x^{-1}} - 2x + 2 by using the following methods, when integration limits are (-2) to (1) 1) Trapezoidal rule using (a) 5 strips, (b) 10 strips, (c) 16 strips 2) Simpson's rule using 8 strips 3) Three-eight rule using 8 strips 4) Gauss quadrature 1 points 5) Gauss quadrature 3 points 6) Drive Gauss quadrature 4 points Q4/ Find the roots of data in (Q1) and find the roots of equation in (Q2) by using the following methods. 1) Bisection method 2) Newton- Raphson method 3) The secant method 4) Modified Newton- Raphson method

          Q1/ Find the interpolation or extrapolation of the following data by using
1) Lagrange formula
2) Gregory-Newton formula
3) Newton's divided difference formula
4) The method of least square of second order

x | -1.5 | 0 | 1.5 | 3 | 4 | 5.5 | 7 | 9
f(x) | -10 | -7 | -0.5 | 8 | 25 | 32 | 44 | 51

Q2/ Find the numerical differentiation of the value x = 0, and x = 4 for the data in (Q1) as follows:
1) Second derivative when using five pointes, two points before point (i) and two points after point (i).
2) Fourth derivative when using five pointes, two points before point (i) and two points after point (i).

Q3/ Find the numerical integration of equation y = xlnx^2 - ^2sqrt{x^{-1}} - 2x + 2 by using the following methods, when integration limits are (-2) to (1)
1) Trapezoidal rule using (a) 5 strips, (b) 10 strips, (c) 16 strips
2) Simpson's rule using 8 strips
3) Three-eight rule using 8 strips
4) Gauss quadrature 1 points
5) Gauss quadrature 3 points
6) Drive Gauss quadrature 4 points

Q4/ Find the roots of data in (Q1) and find the roots of equation in (Q2) by using the following methods.
1) Bisection method
2) Newton- Raphson method
3) The secant method
4) Modified Newton- Raphson method

Q1/ Find the interpolation or extrapolation of the following data by using
1) Lagrange formula
2) Gregory-Newton formula
3) Newton's divided difference formula
4) The method of least square of second order

x | -1.5 | 0 | 1.5 | 3 | 4 | 5.5 | 7 | 9
f(x) | -10 | -7 | -0.5 | 8 | 25 | 32 | 44 | 51

Q2/ Find the numerical differentiation of the value x = 0, and x = 4 for the data in (Q1) as follows:
1) Second derivative when using five pointes, two points before point (i) and two points after point (i).
2) Fourth derivative when using five pointes, two points before point (i) and two points after point (i).

Q3/ Find the numerical integration of equation y = xlnx^2 - ^2sqrtx^-1 - 2x + 2 by using the following methods, when integration limits are (-2) to (1)
1) Trapezoidal rule using (a) 5 strips, (b) 10 strips, (c) 16 strips
2) Simpson's rule using 8 strips
3) Three-eight rule using 8 strips
4) Gauss quadrature 1 points
5) Gauss quadrature 3 points
6) Drive Gauss quadrature 4 points

Q4/ Find the roots of data in (Q1) and find the roots of equation in (Q2) by using the following methods.
1) Bisection method
2) Newton- Raphson method
3) The secant method
4) Modified Newton- Raphson method

Added by Tamara M.

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