The function (x, t) = t 1/2 e x2/t , whose graph is shown in Figure 27,
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The function ƒ(x, t) = t−1/2e−x2/t, whose graph is shown in Figure 27, models the temperature along a metal bar after an intense burst of heat is applied at its center point.
(a) Sketch the vertical traces at times t = 1, 2, 3. What do these traces tell us about the way heat diffuses through the bar?
(b) Sketch the vertical traces x = c for c = ±0.2, ±0.4. Describe how temperature varies in time at points near the center.
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