A one-meter long bar is heated unevenly, with temperaturein C at a distance x meters
Chapter 14, Problem 49(choose chapter or problem)
A one-meter long bar is heated unevenly, with temperaturein C at a distance x meters from one end at time tgiven byH(x, t) = 100e0.1t sin(x) 0 x 1.(a) Sketch a graph of H against x for t = 0 and t = 1.(b) Calculate Hx(0.2, t) and Hx(0.8, t). What is thepractical interpretation (in terms of temperature) ofthese two partial derivatives? Explain why each onehas the sign it does.(c) Calculate Ht(x, t). What is its sign? What is its interpretationin terms of temperature?
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