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To study the contour diagrams (or level curves) of surfaces . " }}{PARA 0 "" 0 "" {TEXT -1 80 "2. To use contour diagrams to fin d whether a function is continuous at a point." }}{PARA 0 "" 0 "" {TEXT -1 11 "3. To use " }{TEXT 371 5 "Maple" }{TEXT -1 52 " to draw \+ a graph and a contour diagram of a surface." }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 0 "" }{TEXT 259 22 " Required Information:" }}{PARA 0 "" 0 "" {TEXT -1 18 "Given a function " }{TEXT 372 1 "z" }{TEXT -1 5 " = \+ " }{TEXT 373 1 "f" }{TEXT -1 1 "(" }{TEXT 374 1 "x" }{TEXT -1 2 ", " }{TEXT 375 1 "y" }{TEXT -1 5 "), a " }{TEXT 376 15 "contour diagram" } {TEXT -1 37 " is defined as the family of curves " }{TEXT 377 1 "c" } {TEXT -1 5 " = " }{TEXT 378 1 "f" }{TEXT -1 1 "(" }{TEXT 379 1 "x" } {TEXT -1 2 ", " }{TEXT 380 1 "y" }{TEXT -1 11 ") in the " }{TEXT 381 3 "x-y" }{TEXT -1 16 " plane, where " }{TEXT 382 1 "c" }{TEXT -1 96 " is a constant. This equation represents the curve obtained a s the intersection of the plane " }{TEXT 383 5 "z = c" }{TEXT -1 20 " with the surface " }{TEXT 384 1 "z" }{TEXT -1 5 " = " }{TEXT 385 1 "f" }{TEXT -1 1 "(" }{TEXT 386 1 "x" }{TEXT -1 2 ", " }{TEXT 387 1 " y" }{TEXT -1 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 42 "or the curve at hei ght c for the surface " }{TEXT 388 1 "z" }{TEXT -1 5 " = " }{TEXT 389 1 "f" }{TEXT -1 1 "(" }{TEXT 390 1 "x" }{TEXT -1 2 ", " }{TEXT 391 1 "y" }{TEXT -1 3 "). " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" } {TEXT 260 18 " Solved Example 1:" }}{PARA 0 "" 0 "" {TEXT -1 41 "1. D raw a graph of each of the surfaces." }}{PARA 0 "" 0 "" {TEXT -1 52 "2 . Draw a contour diagram for each of the surfaces." }}{PARA 0 "" 0 " " {TEXT -1 44 "3. Describe each graph and contour diagram." }}{PARA 0 "" 0 "" {TEXT -1 4 "(a) " }{TEXT 392 2 " z" }{TEXT -1 8 " = 6 + 2" } {TEXT 393 1 "x" }{TEXT -1 4 " + 3" }{TEXT 394 1 "y" }{TEXT -1 12 " \+ (b) " }{TEXT 395 1 "z" }{TEXT -1 5 " = " }{XPPEDIT 18 0 "-x^2-y^ 2;" "6#,&*$%\"xG\"\"#!\"\"*$%\"yGF&F'" }{TEXT -1 12 " (c) " } {TEXT 396 1 "z" }{TEXT -1 8 " = exp( " }{XPPEDIT 18 0 "-x^2-y^2;" "6#, &*$%\"xG\"\"#!\"\"*$%\"yGF&F'" }{TEXT -1 19 ") (d) " } {TEXT 397 1 "z" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "sqrt(x^2+y^2);" "6#- %%sqrtG6#,&*$%\"xG\"\"#\"\"\"*$%\"yGF)F*" }{TEXT -1 25 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 0 "" }{TEXT 261 1 " " }{TEXT 262 9 "Solution:" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT 263 40 " (a) The graph and conto ur diagram of " }{TEXT 398 2 "z " }{TEXT 399 11 " = 6 + 2" }{TEXT 400 1 "x" }{TEXT 401 6 " + 3" }{TEXT 402 1 "y" }{TEXT 403 1 " " }} {PARA 0 "" 0 "" {TEXT -1 33 "We activate the plotting package:" }} {PARA 0 "" 0 "" {TEXT -1 0 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