Unformatted text preview: cannot be done if the points are in diFerent quadrants.) 11. Adapt the proof of Theorem 3.3.4 given in this section for functions of two variables to get a proof for functions of three variables. 3.4 Level Curves A level set of a function f is any subset of its domain of the form L ( f,c ) := { −→ x  f ( −→ x ) = c } where c ∈ R is some constant. This is nothing other than the solution set of the equation in two or three variables f ( x,y ) = c or f ( x,y,z ) = c. ±or a function of two variables, we expect this set to be a curve in the plane and for three variables we expect a surface in space....
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 Calculus, product xy

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