8 Calculus Of Several Variables U Functions Of
Give examples of several surfaces whose level curves are circles and at least one example of a surface whose level curves are not circles (6 points) Math Prompt (include a PDF or image) Find the absolute maximum and absolute minimum of f(x,y) = x xy y2 x on the closed triangular region with vertices (0,0), (2,0) and (0,2)Curves in R2 Graphs vs Level Sets Graphs (y= f(x)) The graph of f R !R is f(x;y) 2R2 jy= f(x)g Example When we say \the curve y= x2," we really mean \The graph of the function f(x) = x2"That is, we mean the set f(x;y) 2R2 jy= x2g Level Sets (F(x;y) = c) The level set of F R2!R at height cis f(x;y) 2R2 jF(x;y) = cg Example When we say \the curve x 2 y = 1," we really mean
