Question

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

\(f\left( {x,y} \right) = \frac{y}{{{x^2} + {y^2}}}\)

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

\(\begin{aligned}{l}f(x,y) &= k\\\frac{y}{{{x^2} + {y^2}}} &= k\end{aligned}\)

Which are circles centered at points on the vertical line\(x = 1.5\)and tangent to x-axis.

Construct graph

By using the software, the graph is: