Question

Draw the function’s graph with its contour map

\(Z = \left( {1 - {x^2}} \right)\left( {1 - {y^2}} \right)\).

Short answer

Answer is not given in the drive

Step-by-step solution

In this function. The parabola\(Z = \left( {1 - {x^2}} \right)\)is the trace in the in the \(xz\)plane and the parabola\(Z = \left( {1 - {y^2}} \right)\)is the trace in the place\(yz\)plane. Hence, graph is as follows:

In the graph, the surface of the function will be near the origin, and contour lines deviate from the origin.

Contour map is: