What is the rate of change of temperature

Reference no: EM13968007

Suppose that T(x,y) 200/ 5+x^2+y^2 represent the temperature at a point (x,y) in the plane. then Tx(x,y) =-400x/5+x^2+y^2 and Ty(x,y)=-400y/5+x^2+y^2 . assume temperature is measured in F and distance in hundreds of miles.

a) what is the temperature at the point (1,2)?

b) if we move from the point (1,2) in direction parallel to the positive y axis what is the rate of change of temperature?

c) if we move from the point (1,2) toward the origin what is the rate of the temperature?

d) what direction gives the greatest rate on change of the temperature at the point (1,2)?

e) what direction gives the lowest rate on change of the temperature at the point (1,2)?

f) find the direction for which the rate of change of the temperature at the point (1,2) is 0.

g) if we moving n the xy plane along the curve r(t)=t(i)+2t^2(j), where t is measured in hours what is the rate of change of temperature with respect to time as we pass through the point (1,2)?

Reference no: EM13968007

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