Question

Draw a Contour Map of the function showing several level Curves.

\(f\left( {x,y} \right) = y\sec x\)

Short answer

The contour map is:

Step-by-step solution

Assume a constant

Let us remember that the level curves of a function of several variables shows where the graph of function has height k, where k is the z-value of level curve.

The level curves of given function are

\(\begin{aligned}{l}f(x,y) &= k\\y\sec x &= k\\y &= \frac{k}{{\sec x}}\\y &= k\cos x\;\;\;\end{aligned}\)

Which are cosinusoidal functions

Construct Graph

The level curves for\(k = 1,2,3,4\)are shown on the following graph: