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uestion. i5% For the purpose of shrinking a trunnion into a hub, the reduction of diameter D of a trunnion shaft by cooling it through a temperature change of AT is given by where D original diameter (in.), and = coefficient of thermal expansion at average ternperature (in/in/ The trunnion is cooled from 80F to -108F, giving the average temperature as -14F. The table of the coefficient of thermal expansion vs. temperature data is given in the table below Thermal Expansion Coefficient, (in/in/oF) 6.47 x 10-6 6.00 x 10- 5.58 x 10-6 4.72 10-6 3.58 x 10-6 2.45 10-6 Tennperature T(*F) 80 -60 160 260 -340 Using MATLAB software answer the following parts of the question (a) If the coefficient of thermal expansion needs to be calculated at the average temperature of -14F, determine the value of the coefficient of thermal expansion at T14F using the best possible second and third order Lagrange polynomials (b) Find the relative approximate error for the second order Lagrange polynomial approximation. uestion. i5% For the purpose of shrinking a trunnion into a hub, the reduction of diameter D of a trunnion shaft by cooling it through a temperature change of AT is given by where D original diameter (in.), and = coefficient of thermal expansion at average ternperature (in/in/ The trunnion is cooled from 80F to -108F, giving the average temperature as -14F. The table of the coefficient of thermal expansion vs. temperature data is given in the table below Thermal Expansion Coefficient, (in/in/oF) 6.47 x 10-6 6.00 x 10- 5.58 x 10-6 4.72 10-6 3.58 x 10-6 2.45 10-6 Tennperature T(*F) 80 -60 160 260 -340 Using MATLAB software answer the following parts of the question (a) If the coefficient of thermal expansion needs to be calculated at the average temperature of -14F, determine the value of the coefficient of thermal expansion at T14F using the best possible second and third order Lagrange polynomials (b) Find the relative approximate error for the second order Lagrange polynomial approximation