Unformatted text preview: a and b (measured in cm) and both sides are increasing at the rate of 1 cm/sec. If the area of the triangle remains constant, at what rate is the angle θ between a and b changing when θ = π 6 , a = 4, and b = 3? 4. The temperature at each point of a metal plate is given by the function T ( x,y ) = 100 e-x 2-3 y 2 , where T is measured in degrees Celsius and x and y are measured in meters. (a) If an object at the point (3, -1) moves toward the point (1,2), does the temperature increase or decrease? At what rate? (b) Starting from the point (3, -1), in what direction does the temperature increase most rapidly? What is the rate of change in this direction? (c) Starting from the point (3, -1), in what direction does the temperature decrease most rapidly? What is the rate of change in this direction? 1...
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This note was uploaded on 10/14/2009 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.
- Spring '07