Given a function f : [0,1] -> R defined as: f(y) = y2 + y + 1 Find a function g where gb) = y + b , where a, b E R and gly) is the best approximation of f(y) in the L2 -norm. Assume that f : R-> R is an analytic function. (1) Analyze and derive the expression for the error: fly) [fy + k) - f(-k)] ~21r6y+k (2) Use Richardson Extrapolation approach from part (1) to create a new finite difference approximation that have a higher order. (3) Use Newton-Cotes Procedure approach to construct a quadrature rule for all polynomials of degree 2 that has the following form: SFV) dy z Af(a) +Bf (**) + Cf(b) given a = 4, b = 8 2k a+b Given a function f : [0,1] -> R defined as: f(y) = y2 + y + 1 Find a function g where gb) = y + b , where a, b E R and gly) is the best approximation of f(y) in the L2 -norm. Assume that f : R-> R is an analytic function. (1) Analyze and derive the expression for the error: fly) [fy + k) - f(-k)] ~21r6y+k (2) Use Richardson Extrapolation approach from part (1) to create a new finite difference approximation that have a higher order. (3) Use Newton-Cotes Procedure approach to construct a quadrature rule for all polynomials of degree 2 that has the following form: SFV) dy z Af(a) +Bf (**) + Cf(b) given a = 4, b = 8 2k a+b