Answer
a. $D$
b. $V$
Work Step by Step
This f(x,y) is not periodic. By system of elimination, we eliminate the periodic functions, A, C, E and F. This leaves B and D. B has parabolas as traces in the xz and yz planes, but when y=0, $\displaystyle \frac{x}{1+x^{2}}$ is not a parabola.
Therefore, graph D is the only one remaining.
The level curve graph V is the correct choice, because when we move away from the origin, the denominator in f(x,y) becomes big, and z approaches 0. This means that, for equal increments in x and y, the level curves will be farther apart as we move farther from the origin, as they are in (V).
