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- The linearization of ex at x = 1 Estimate to five decimal places the magnitude of the error involved in replacing ex by 1 + x on the interval [0, 0.2]Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step sizesof h1 = π/ 3 and h2 = π/ 6. Employ centered differences of O(h2) for the initial estimates.Suppose that the total cost of manufacturing x units of a certain commodity isC (x) = 2?2 + 6? + 12. Use differentials to approximate the cost of producing the 21st unit.Compare this estimate with the cost of actually producing the 21st unit
- In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after beforeFind the equation of normal to the function f(x)=x3−3x+1�(ignore the symbol, its just 1) at its local maximum point.Find the equation of the normal line to f(x) = 2^x log2(x) when x = 1
- From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)Compute forward and backward difference approximations of O(h) and O(h2), and central difference approximations of O(h2) and O(h4) for the first derivative of y = cos x at x = π/4 using a value of h = π/ 12.Estimate the true percent relative error εt for each approximation.2. Find the derivative of f(x, y, z) = x³ – xy2 – z at Po(1,1,0) in the direction of V = 2ỉ – 3j + 6k. In what direction does f(x, y, z) change most rapidly at Po and what are the rates of change in these directions?