Lagrange’s formula

      Answer all the questions Q.1 Find the root of the equation [5 Marks] x^2=-4sinx Correct to three decimal places using Method of false position and Newton-Raphson method. Q.2 Solve the following system using Gauss Jacobi method and correct your answer to three decimal places. [6 Marks] 3x+y+z=4 x+4y-z=-5 x+y-6z=-12 Q.3 Solve the following system using Gauss Jordan method. [7 Marks] 10x+y-z=12 2x+10y+z=13 x+y+5z=7 Q.4 Find the value of y when x=6, using Lagrange’s formula from the following table [6 Marks] x 1 2 3 4 7 y 2 4 8 16 128 Q.5 Find the cubic polynomial from the following table using Newton’s divided difference formula and then find f(4). [6 Marks] x 0 2 3 5 6 y 1 19 55 241 415