Question

On a particular day, the temperature in Tahoe is given by T(?, ?) = uv^2( where the origin is located at the Northstar lodge. Distances are measured in miles.

a). If I start at the location (u, v)= (1, 1), give the unit vector associated with the direction (in the domain) I should go to warm up as quickly as possible.

b). What is the rate of change of the temperature in this direction?

c). At the same location, give the unit vector(s) associated with the direction (in the domain) I should go to stay at the same temperature.

d). Use a directional derivative to estimate the change in temperature if I start at the point ?0 = (1,1) in

the domain and move a distance of sqrt(0.5)miles toward the point ?1 = (−1,3)

Answer #1

The temperature at a point (x,y,z) is given by
T(x,y,z)=200e−x2−y2/4−z2/9, where T is measured in degrees celsius
and x,y, and z in meters. There are lots of places to make silly
errors in this problem; just try to keep track of what needs to be
a unit vector. A. Find the rate of change of the temperature at the
point (0, -1, 2) in the direction toward the point (-1, 4, 2). b)In
which direction (unit vector) does the temperature...

The temperature at a point (x,y,z) is given by
T(x,y,z)=200e−x2−y2/4−z2/9, where Tis measured in degrees celcius
and x,y, and z in meters. There are lots of places to make silly
errors in this problem; just try to keep track of what needs to be
a unit vector.
Find the rate of change of the temperature at the point (0, 1, -2)
in the direction toward the point (-1, -2, 5).
In which direction (unit vector) does the temperature increase the...

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