Approximate the integral using Simpson's 1/3 rule and calculate the percentage error. (Take result up to 4 decimal places)
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Construct a forward difference table for the following values
x 0.1 0.3 0.5 0.7 0.9 1.1 1.3
y 0.003 0.067 0.148 0.248 0.37 0.518 0.697

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Solve the system

by Gauss Seidal Method, taking (0, 0, 0)t as initial approximation(Two iterations only and take result up to 4 decimal places )

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Let , use cubic Lagrange interpolation based on the nodes to approximate f(1.5) and f(1.3).

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Approximate the Dominant Eigenvalue and corresponding Eigenvector for the matrix

by using Power Method. Start with . (Five iterations only and take result up to 4 decimal places)

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