## Thomas' Calculus 13th Edition

Domain: x, y can be any real numbers in the x-y plane. Range: $f(x,y) \gt 0$ Level Curves: $x+y = \ln{c}$ (constant),
Function: $f(x,y) = e^{x+y}$ Domain: x, y can be any real numbers in the x-y plane. Range: $f(x,y) \gt 0$ Level Curves: $f(x,y) = c$ (constant), $e^{x+y}=c$ $\ln{e^{x+y}}=\ln{c}$ $x+y = \ln{c}$ (constant) Hence, the level curves are a series of straight lines. For example, when $c=e$, $x+y = 1$ which is shown in the figure.