Given a multivariable temperature function and the graph of its level curves: De
ID: 3028305 • Letter: G
Question
Given a multivariable temperature function and the graph of its level curves:
Describe a possible graph of the temperature, T, on an east-west line through Durango, Colorado, if the origin is at Durango, the positive x-axis corresponds to east of Durango, and the vertical z-axis is the temperature. For negative x within a hundred miles or the origin, the sign or T'(x) is while tor positive x a few hundred miles from the origin, the sign of T'(x) is. We estimate that T(0) = degrees Fahrenheit. (b) Describe a possible graph of the temperature, T on a north-south line through Moines Iowa if the origin is at Moines, the positive y-axis corresponds to north of Moines, and the vertical z-axis is the temperature For negative y within a few hundred miles of the origin, the sign of T'(y) is. while for positive y a few hundred miles from the origin, the sign of T'(y) is. We estimate that T(0) = degrees Fahrenheit.Explanation / Answer
a) Looking at the graph as we go left or west side of the Durango, Colorado, we meet the regions passing through larger temperature lines which shows temperature is increasing.
So, sign of T'(x) is +ve as we go on the negative X axis
As we go along the positive axis we keep getting closer to the 50F line which is less than 55F showing us a decrease in the temperature,
So, sign of T'(x) is -ve as we go along the positive X axis
T(0) = 55 as Durango passes through the 55F tempereture curve
b)
Des Monies lies between the 50F and 55F temperature lines
As we go up the positive Y axis we keep getting nearer to the 50F curveshowing a decrease in the tempereture
So, sign of T'(y) as we move along the positive Y axis is -ve
Similalrly as we move along the negative Y axis sign of T'(y) changes to +ve
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