Find y and dy/dx at x = 1 using Newton’s forward difference formula for the given data:

Evaluate the integral using the Trapezoidal Rule.

Integral unclear in the scan.

State and prove Simpson’s Three-Eighth Rule.

Solve the equations using the Matrix Inversion Method.

Equations unclear in the scan.

Solve the following system of equations:

Solve the following equations by the Gauss-Jacobi method.

Equations partly unclear in the scan.

Solve the differential equation using the Taylor Series Expansion Method, given y(0) = 1.

Differential equation partly unclear in the scan.

Compute y(0.2) using Euler’s Method.

Differential equation and initial condition unclear in the scan.

Find the first and second derivatives at x = 1.6 from the following table.

Table not legible in the scan.

Find f(1.5) from the following table:

Table partly lost in the scan.

Evaluate ∫ x log x dx using Simpson’s Rule.

Evaluate the required integral using the tabulated values:

x-values and integral unclear in the scan.

Evaluate the integral using Weddle’s Rule.

Integral and limits unclear in the scan.

Solve the equations using the Matrix Inversion Method:

Second equation unclear in the scan; shown as the likely reading.

Solve the system of equations using the Gauss-Jordan Method:

Solve the equations using the Jacobi Method, correct to 3 decimal places.

Equations partly unclear in the scan.

Solve the equations using the Factorization Method:

Solve the following equations by the Gauss method:

Remaining equations unclear in the scan.

Given y′ = y with y(0) = 1, compute y(0.1) and y(0.2) using Picard’s Method.

Given the differential equation in x and y with y(0) = 0, find y(0.2), y(0.4) and y(0.6) using the Runge-Kutta Fourth Order Method.

Differential equation unclear in the scan.