14.1.1 Level Sets 240220

(3) Plot the level sets for values of c from 0 to 3, increasing in increments of 0.5.

Expression 11: "f" left parenthesis, "x" , "y" , right parenthesis left brace, "z" equals "I" , right brace

Expression 12: "I" equals left bracket, 0 , 0.5 , ... , 3 , right bracket

Expression 13: "C" Subscript, "o" "l" "o" "r" , Baseline equals hsv left parenthesis, "h" , 1 , 1 , right parenthesis

Expression 14: "h" equals negative StartFraction, 340 Over max left parenthesis, "I" , right parenthesis minus min left parenthesis, "I" , right parenthesis , EndFraction left parenthesis, "I" minus min left parenthesis, "I" , right parenthesis , right parenthesis plus 340

(4) Imagine raising a level set (level curve) of value c into 3D up to the plane z=c.

To see what you get, hit the "xyz-space" icon (instead of "xy-plane" icon.

Next hit the dot below to graph the z=f (x,y).

Expression 18: "f" left parenthesis, "x" , "y" , right parenthesis equals StartRoot, 9 minus "x" squared minus "y" squared , EndRoot

All Done .