Approximation of Functions

Let f(x)=invertedCOS(x) for EQUATION1 (the principal branch of EQUATION2) Find the polynomial of degree two EQUATION3 which minimizes EQUATION4. *(Please see attachment for all equations)

Numerical Integration

Let P2(x) be the quadratic polynomial interpolating f(x) at x= ... Use a Taylor series expansion of f(x) to show (FORMULA) (SEE ATTACHMENT FOR COMPLETE PROBLEM)

Numerical Integration - Two-point Gaussian Quadrature

Derive the two-point Gaussian quadrature formula for: I(f) = integration from 0 to 1 of f(x)log(1/x)dx (See attachment for full question)

Numerical Integration - Two-point Gaussian Quadrature

Derive the one and two point Gaussian quadrature formula for... with weight function w(x)=x

showing matrix norm

The frobenius norm (which I know is not a natural norm)is defined for an n x n matrix A by ||A||_f = (sum i=1 to n, sum j=1 to n, |a_ij|^2)^1/2 Please show that ||.||_f is a matrix norm. That is, satisfy the five axioms. NOte: _ is subscript