Exam 14: Partial Derivatives

Find the limit

Use partial derivatives to find the implicit partial derivatives and

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Find for the function

Evaluate the limit.

Two contour maps are shown. One is for a function f whose graph is a cone. The other is for a function g whose graph is a paraboloid. Which is the contour map of a cone?

Find the differential of the function.

Suppose that over a certain region of space the electrical potential V is given by . Find the rate of change of the potential at in the direction of the vector .

Find the maximum rate of change of f at the given point.

Let Find

Find the first partial derivatives of the function .

The temperature-humidity index I (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write I = f (T, h). The following table of values of I is an excerpt from a table compiled by the National Oceanic and Atmospheric Administration. For what value of T is ?