The temperature at the point (x, y) in the plane is givenby F(x, y)=1/(x2 + y2). A
Chapter 17, Problem 47(choose chapter or problem)
The temperature at the point (x, y) in the plane is givenby F(x, y)=1/(x2 + y2). A ladybug moves along aparabola according to the parametric equationsx = t, y = t2.Assuming that the ladybugs temperature is the same asthe plane at her current location, find the rate of changein the temperature of the ladybug at time t. Use the chainrule to show that for any temperature function F(x, y)and any path of the ladybug r = x(t)i + y(t)j , thenwriting v (t) = dr /dt gives:Rate of change of temperature = F(x, y) v .
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