Experiments show that in a temperature field, heat flows in the direction of maximum decrease of temperature

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Experiments show that in a temperature field, heat flows in the direction of maximum decrease of temperature T. Find this direction in general and at the given point P. Sketch that direction at P as an arrow.

Graph some curves of constant temperature (“isotherms”) and indicate directions of heat flow by arrows when the temperature equals

(a) x3 - 3xy2

(b) sin x sinh y

(c) ex cos y.

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