Legendre polynomial least square approximation

Using Legendre polynomials of degree 1, 2, and 3, find the least-squares approximation for the function e^(−x) on [2, 4]. I am confused as to how to do this on the interval [2,4] and not [-1,1] I have included the notes on this section, including an example.

Convergence and Error Analysis

Word Doc also attached, easier to view. Please give the complete solution, include reasoning and calculations used to arrive at answer.

Lagrange Polynomial Interpolation

Please see the attached problem. (Word and pdf attached). Please give the complete solution, include reasoning and calculations used to arrive at answer. If you use a particular theorem please identify it. We cannot use any high level command from Maple, Mathematica or MatLab.

Doolittle LU decomposition

Please see the attached problem: Please give the complete solution, include reasoning and calculations used to arrive at answer.

Third Order Taylor Method

Please see problem attached.