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5.Which of the following represents the correct Taylor series expansion for 𝑓𝑓𝑖𝑖−3using 𝑥𝑥=𝑥𝑥𝑖𝑖as the referencepoint?AMME2000/AMME29602018QuizSolutions,Page3 of6
6.Thevoltageinauniformconductorisgovernedbythedifferentialequation:Vt=1RCVxx(1)whereVis the voltage,R= 10000 Ω is the resistance andC= 3×10-3F is the capacitance. In a 1 mlong conductor, the voltage at both ends of the conductor is regulated to be a constant of 0 V and theinitial voltage distribution takes the form shown in Figure 1.00.20.40.60.810246810Figure 1: Initial voltage distribution.(a)Clearly state mathematically the boundary conditions and initial condition of the problem.(b)Using separation of variables, derive the exact solution to this problem, clearly stating the valuesof any parameters in the Fourier Series coefficients.AMME2000/AMME29602018QuizSolutions,Page4 of