The Importance of Happiness in Life's Purpose, Exercises of Ethics

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“WHAT EVER YOU DO, ALWAYS CHOOSE WHAT MAKES YOU HAPPY” Question Machine Exercise: a. Make an Algorithm for interpolating, approximating, and root-finding using the methods below: « Lagrange's Method + Newton's Method Neville's Method Interpolation with Cubic Spline + Linear Fit Polynomial Fit Exponential Fit + Bisection Method + False Position and Secant Methods + Newton-Raphson Method b. Solve the following problems (you can use hand calculation) 1. Use Lagrange interpolation and Newton interpolation methods to find a cubic polynomial that interpolates the following data points: {(-2, -3), (-1, 1), (0, -1), (1, -3)}. After applying each of these methods, convert the polynomial to the standard form P(x) = ag + a4x + aox? + a3x? (if it is not already in this form). 2. Given the set of data points {(-3, -1), (-2, 1), (O, 2), (1, 3), (3, 2)}, fit a straight line y = mx + b that approximates the points in the least-squares sense. (a) Write a least-squares system Ax = b which can be used to obtain values for m and b. (b) Solve the obtained system above using the method of normal equations. Answer “THE PURPOSE OF LIVES IS TO BE HAPPY, SO ENJOY EVERYTHING”