These are the questions will you plz help

Q1 Prove that the interpolating polynomial for the following data is of degree 3 X [13 marks] 1( x) 3 3 4 5 7 10 31 69 1011 Hence, interpolate at x = 3.5 and x = 6. Also find, f (5) and f" (3). 131 351 [12 marks] [Total marks 25] 02 Solve the following system of equations using THREE iterations of the Gauss- Seidel iteration method. [18 marks] x+ 3y+52z=174, x- 27y+ 2z =71, 41x - 2v+ 3z =65 Start with x = 1, v= - 1, z = 3 Compute the error of each iteration. [7 marks] [Total marks 251 Q3 The velocity of a particle which starts from rest is given by the following table. 1 (sec ) 0 2.25 4.5 6.75 9.00 11.25 13.50 15.75 18.00 v (m/sec) 0 12 16 26 40 44 12 5 0 Evaluate using trapezium rule, the total distance travelled. [13 mark Improve the result using Romberg integration. [12 mar