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 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 Q03 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 Q04 Unique polynomial f(x) of degree 2 or less such that f (0) = 1, 1 f(1) = 3 and f(3) = 55 is English · UPPSC GDC 2021 Q05 Using Euler's modified method. the value of y(0.02) for the differential equation () 2 dy x y,y 0 1 dx = + = and ta... English · UP Higher Asst. Prof. 2021 Q06 If y (0) = 3, y (1) = 10, y(2) = 18, y(3) = 30 and y(4) = 50, then value of ∆ ∆ ∆4 y(0) is English · UPPSC GDC 2021