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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)[2]Clearly state mathematically the boundary conditions and initial condition of the problem.(b)[6]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
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