Functions Of Several Variables

  1. Find and sketch the domain of the function

    fxy=1+xy2 .

    Find the range of f .

  2. Make a rough sketch of a contour map for the function whose graph is shown.

    two hills

  3. Draw a contour map of the function fxy=ylnx showing several level curves.
  4. Sketch the contour map and the graph of the function fxy=x2+9y2 .
  5. Match each given function with its graph and its contour map. Explain.

    1. z=sinxy
    2. z=excosy
    3. z=sinxy
    4. z=sinxsiny
    5. z=1x21y2
    6. z=xy1+x2+y2
    1. xy surface
    2. xy surface
    3. xy surface
    4. xy surface
    5. xy surface
    6. xy surface
    1. contour map
    2. contour map
    3. contour map
    4. contour map
    5. contour map
    6. contour map
  6. Describe the level surfaces of the function fxyz=x2y2+z2 .
    Family of hyperboloids of one or two sheets with axis the y-axis .