Chapter 12.2, Problem 43E

Resistors in parallel Two resistors wired in parallel in an electrical circuit give an effective resistance of $R(x,y)=\frac{x}{x+y}$, where x and y are the positive resistances of the individual resistors (typically measured in ohms).

a.    Graph the resistance function using the window [0, 10] × [0, 10] × [0, 5].

b.    Estimate the maximum value of R, for 0 < x ≤ 10 and 0 < y ≤ 10.

c.    Explain what it means to say that the resistance function is symmetric in x and y.