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1. Given a cubic spline interpolation: (S.(x) = 1-2x - x3 0<x< 1 S(x) = 15,(x) = 2 + b(x - 1) + c(x - 1)2 + d(x - 1)2 15x<2 determine constants b, c, and d so that all conditions for a natural cubic spline hold. 2. Given the following data: X 0 1 0.25 1.4 0.5 1.6 1 2 у Consider the problem of constructing a natural cubic spline S(x). Form the matrix A and vector of y values which are used to solve the vector containing all coefficients