Math Chapter Wise question with answer

Q01 Let φ:[0, 1] → → → ℝ be three times continuously differentiable. Suppose that the iterates defined by xn+1 = φ(xn),... English · Bihar (TRE 1.0) -2023 Q02 While solving the equation x2 – 3x + 1 = 0 using the Newton-Raphson method with the initial guess of a root as 1, t... English · Bihar (TRE 1.0) -2023 Q03 Consider the system of equations 1 2 3 5 2 1 x 13 -2 5 2 x = -22 -1 2 8 x 14 With the initial guess of the solution... English · Bihar (TRE 1.0) -2023 Q04 For what values of α and β, the quadrature formula ∫ 1 -1 f(x)dx = αf(-1) + f(β) is exact for all polynomials of de... English · Bihar (TRE 1.0) -2023 Q05 The value of the integral () ∫ 1 2 -1 I = exp x dx Using a rectangular rule is approximated as 2. Then, the approxi... English · Bihar (TRE 1.0) -2023 Q06 Let y be the solution of the initial value problem () () 2 d y + y = 6cos2x,y(0) = 3,y' 0 = 3,y' 0 = 1 dx Let the L... English · Bihar (TRE 1.0) -2023