Section 14.3 Partial Derivatives

The wind-chill index \(W\) is the perceived temperature when the actual temperature is \(T\) and the wind speed is \(v\), so we can write \(W = f(T, v)\). The following table of values is an excerpt from Table 1 in Section 14.1.

1. Estimate the values of \(f_T(-15, 30)\) and \(f_v(-15, 30)\). What are the practical interpretations of these values?

2. In general, what can you say about the signs of \(\partial W/\partial T\) and \(\partial W/\partial v\)?

3. What appears to be the value of the following limit?

\[ \lim_{v \to \infty} \frac{\partial W}{\partial v} \]