restart:Tangent Planes to Level SurfacesMaplet by Cangelose and DavidsonCorrections by Yasskin:surface must be an equationmodified text and captionsimproved colorsthepoint was pointlessFixed the hint.It is not the partial derivative of x. It is the partial derivative of f with respect to x.with(Maplets[Elements]):with(Maplets[Tools]): with(plots): with(student): with(linalg): with(plottools):
StartEngine();lightorange := "#FFB300":randomize():great := [" Great job! "," Right on the mark. "," Great. "," That's absolutely right. "," Awesome. You're unstoppable. "," Correct. "," WOW, nailed that one. "," You got it! "," YES! Right on. "," Way to go. "," Don't stop now. "," I knew you could do it! "," Perfect. You're unstoppable. "," Radical Dude. "," Power house. "," Sweet! Keep on Rockin'. "," You rock! "," You got those mad skills. "," Awesome! "," Wowzers! That was great! "," Awesome man! "," Good job! You really know what you are doing. "," You're awesome kid. "," Tearing it up. "," Right on the money. "," High Five!!!!! "," What a nerd! "," You're so money. "," You're a genious. "," You hit the nail on the head. "," Excellent! "," If I had a cookie, I'd give it to you. "," You're a winner. "," That's a winner. "," Whoop! Way to go. "," That's the way, ah ha ah ha, I like it. "," Oh yeah! "," You're the bomb! "," That was fantastic! "," Oh Snap! "," That's krunk! "]:randgreat := rand(1..nops(great)):nextquest := ["Keep it up.","Keep going.","On to the next function.","Try another function.","Find another tangent line."]:randnext := rand(1..nops(nextquest)):sorry := [" Sorry, that's not right. "," Nope, but don't give up. "," Not quite, it's a little off. "," Bummer, thought you would get it this time. "," Close, but no cigar. "," Slightly off. "," If you need help, please ask a human. "," I don't know where you went wrong. "," Sorry, killer problem. "," No, but don't blow it off. "," D'oh! "," That's whack. "," Yikes! Really close. You'll get it next time. "," Puma! Thought you would get it this time. "," Nice try, but your answer is wrong. "," Ask your neighbor for help, just not if this is a quiz, THAT would be cheating. "," Brutal kid. "," That won't fly, try to be more like Superman. "," So close and yet so far. "," So, that was just practice. "," Ooooh...close. "," A swing and a miss. "," Better luck next time. "," Oops. "," Tilt. Play again. "," I know you can do better. "," Sorry, you're not as great as Lisa the Great "," Better luck next time. "," Tisk, tisk. It's a tough one. "," It takes a lot of wrongs to make a right. "," Even Einstein didn't get everything right. "," Oh man, you were so close. "," Today's not your lucky day. "," Don't quit your day job. "," You're colder than a polar bear's toenail. "]:randsorry := rand(1..nops(sorry)):tryagain := ["Try the hint.","Fix your answer and check it again.","Give it another try.","Try again.","Please try again."]:randtry := rand(1..nops(tryagain)):showit := [" OK That's just practice. But try doing it yourself."," That's fine for practice. Try doing it yourself."," Read the hint and enter an answer yourself."," So that was practice. Try doing it yourself."]:randshow := rand(1..nops(showit)):### here are the functions and the values for the functions###i:=0:i:=i+1;funcs[i]:=x^2+4*y^2-z;A[i]:=[[-3,2,1],[5,2,9],[2,5,6],[8,4,7],[8,0,6]]:
mini[i]:=[[-6, -1,-2], [2,-1,6], [-1,2,3], [5,1,4],[5,-3,3]]:
maxi[i]:=[[0,5,4], [8,5,12], [5,8,9],[11,7,10],[11,3,9]]:randpt[i]:=rand(1..nops(A[i])):i:=i+1;funcs[i]:=x^2-y^2+z^3;A[i]:=[[9,5,6],[4,4,3],[9,3,3],[5,7,1],[1,1,2]]:
mini[i]:=[[6,2,3],[1,1,0],[6,0,0],[2,4,-2],[-2,-2,-1]]:
maxi[i]:=[[12,8,9],[7,7,6],[12,6,6],[8,10,4],[4,4,5]]:randpt[i]:=rand(1..nops(A[i])):
i:=i+1;funcs[i]:=exp(x)+exp(y)*exp(z);A[i]:=[[-3,1,1],[ln(5), ln(2), ln(1)]]:
mini[i]:=[[.001,.001,.001],[.001,.001,.001]]:
maxi[i]:=[[4,4,4], [4,3,3]]:randpt[i]:=rand(1..nops(A[i])):i:=i+1;funcs[i]:=x^2+y^2+z^2;A[i]:=[[0, 6, 4], [3, 2, 6], [4, 3, 2], [6, 4, 3], [2,0,1]]:
mini[i]:=[[-3,3,1],[0,-1,3],[1,0,-1],[3,1,0],[-1,-3,-2]]:
maxi[i]:=[[3,9,7],[6,5,9],[7,6,5],[9,7,6],[5,3,4]]:randpt[i]:=rand(1..nops(A[i])):i:=i+1;funcs[i]:=sin(x*y)+z;A[i]:=[[0, Pi/6, 1], [3, Pi/2, 0],[Pi,1,1]]:
mini[i]:=[[-.5,0,0],[2.5,1,-.5],[.5,.5,2.5]]:
maxi[i]:=[[.5,.5,2],[3.5,1.8,.5],[1.5,1.5,3.5]]:randpt[i]:=rand(1..nops(A[i])):i:=i+1;funcs[i]:=x^2*y^3-cos(z);A[i]:=[[-3, -2, 3*Pi/2], [5,4,Pi/2], [1, 2, 2*Pi]]:
mini[i]:=[[-6,-5,0],[2,1,-2],[-2,-1,3]]:
maxi[i]:=[[0,1,3*Pi],[8,7,3*Pi/2],[4,5,6*Pi]]:randpt[i]:=rand(1..nops(A[i])):i:=i+1;funcs[i]:=x^4+y*z;A[i]:=[[1, 2, 4], [3, 4, 5], [3,9,2]]:
mini[i]:=[[-2,-1,1],[4,-2,2],[0,3,5]]:
maxi[i]:=[[4,5,7],[10,4,8],[6,9,11]]:randpt[i]:=rand(1..nops(A[i])):randfunc := rand(1..i):
i:='i':
Show_Function := proc()
local pointi, minif, maxif, mysubs, fabc, Nx, Ny, Nz, fgraph, tgraph;
global randfunc, whichfunc, funcs, func, A, randpt, whichpoint, x, a, dfx, dfy, dfz, functan;
options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`;
whichfunc := randfunc();
func := funcs[whichfunc];
##assigning the function we're working with##
pointi:=randpt[whichfunc](); ##picking a random point##
a := A[whichfunc][pointi];
minif:=mini[whichfunc][pointi];
maxif:=maxi[whichfunc][pointi];
mysubs:=equate([x,y,z],a);
fabc:=subs(mysubs,func);
dfx := diff(func,x);
##partial of f wrt x##
Nx:=subs(mysubs, dfx):
##partial of f wrt x at a##
dfy := diff(func,y);
##partial of f wrt y##
Ny:=subs(mysubs, dfy):
##partial of f wrt y at a##
dfz := diff(func,z);
##partial of f wrt z##
Nz:=subs(mysubs, dfz):
##partial of f wrt z at a##
functan:= Nx*(x-a[1])+Ny*(y-a[2])+Nz*(z-a[3]):
##tangent plane##
fgraph:=implicitplot3d(func=fabc,x=minif[1]..maxif[1], y=minif[2]..maxif[2], z=minif[3]..maxif[3], color=red):
##graph of f##
tgraph:=implicitplot3d(functan=0, x=minif[1]..maxif[1], y=minif[2]..maxif[2], z=minif[3]..maxif[3], color=green):
##graph of tangent plane##
Set('myplot' = display(fgraph,tgraph, axes=normal)):
Set('fMML' = (func=fabc)): Set('pointMML' = a): Set('fx' = ""): Set('fy' = ""): Set('fz' = ""): Set('ftan' = ""): Set('fxck' = "", 'fxck'(background)=white, 'fxck'(foreground) = black): Set('fyck' = "", 'fyck'(background)=white, 'fyck'(foreground) = black): Set('fzck' = "", 'fzck'(background)=white, 'fzck'(foreground) = black): Set('ftanck' = "", 'ftanck'(background)=white, 'ftanck'(foreground) = black): Set('reply' = "", 'reply'(background)=white, 'reply'(foreground) = black): if whichfunc = 3 then Set('reply' = "Enter the exponential function as exp(x).", 'reply'(background)=lightorange, 'reply'(foreground) = black) end if;end proc:Check_fx := proc() local user_fx; global dfx, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; user_fx := Get('fx'::algebraic, corrections=true, update=true): Set('reply' = "", 'reply'(background)=white, 'reply'(foreground) = black); if simplify(normal(dfx - user_fx))<> 0 then Set('fxck' = "incorrect", 'fxck'(background)=red, 'fxck'(foreground) = white): else Set('fxck' = " correct ", 'fxck'(background)=green, 'fxck'(foreground) = black): end if;end proc:Show_fx := proc() global dfx, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; Set('fx' = dfx): Set('fxck' = " shown ", 'fxck'(background)=lightorange, 'fxck'(foreground) = black): Set('reply' = showit[randshow()], 'reply'(background)=lightorange, 'reply'(foreground) = black):end proc:Check_fy := proc() local user_fy; global dfy, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; user_fy := Get('fy'::algebraic, corrections=true, update=true): Set('reply' = "", 'reply'(background)=white, 'reply'(foreground) = black); if simplify(normal(dfy - user_fy))<> 0 then Set('fyck' = "incorrect", 'fyck'(background)=red, 'fyck'(foreground) = white): else Set('fyck' = " correct ", 'fyck'(background)=green, 'fyck'(foreground) = black): end if;end proc:Show_fy := proc() global dfy, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; Set('fy' = dfy): Set('fyck' = " shown ", 'fyck'(background)=lightorange, 'fyck'(foreground) = black): Set('reply' = showit[randshow()], 'reply'(background)=lightorange, 'reply'(foreground) = black):end proc:Check_fz := proc() local user_fz; global dfz, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; user_fz := Get('fz'::algebraic, corrections=true, update=true): Set('reply' = "", 'reply'(background)=white, 'reply'(foreground) = black); if simplify(normal(dfz - user_fz))<> 0 then Set('fzck' = "incorrect", 'fzck'(background)=red, 'fzck'(foreground) = white): else Set('fzck' = " correct ", 'fzck'(background)=green, 'fzck'(foreground) = black): end if;end proc:Show_fz := proc() global dfz, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; Set('fz' = dfz): Set('fzck' = " shown ", 'fzck'(background)=lightorange, 'fzck'(foreground) = black): Set('reply' = showit[randshow()], 'reply'(background)=lightorange, 'reply'(foreground) = black):end proc:Check_ftan := proc() local user_ftan; global functan, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; user_ftan := Get('ftan'::algebraic, corrections=true, update=true): if simplify(normal(functan - user_ftan))<> 0 then Set('ftanck' = "incorrect", 'ftanck'(background)=red, 'ftanck'(foreground) = white): Set('reply' = cat(sorry[randsorry()], tryagain[randtry()]), 'reply'(background)=red, 'reply'(foreground) = white): else Set('ftanck' = " correct ", 'ftanck'(background)=green, 'ftanck'(foreground) = black): Set('reply' = cat(great[randgreat()], nextquest[randnext()]), 'reply'(background)=green, 'reply'(foreground) = black): end if;end proc:Show_ftan := proc() global dfz, x; options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`; Set('ftan' = functan): Set('ftanck' = " shown ", 'ftanck'(background)=lightorange, 'ftanck'(foreground) = black): Set('reply' = showit[randshow()], 'reply'(background)=lightorange, 'reply'(foreground) = black):end proc:Hint := proc()global a;options `Copyright 2006, Philip B. Yasskin, Texas A&M Univ.`;Set('reply' = cat("The tangent plane is Nx (x-a) + Ny (y-b) + Nz (z-c) = 0.\nNote: Nx = df/dx(a,b,c) which is the partial derivative of f with respect to x evaluated at (a,b,c)."), 'reply'(background)=lightorange, 'reply'(foreground) = black):end proc:Tangent_Line := Maplet(onstartup = RunWindow(MAIN), Font[helv10]("helvetica",10),Window[MAIN]( 'title'="Tangent Planes to Level Surfaces", 'defaultbutton'='BHint',
[ halign=none, background=wheat,
[ halign=none, background=wheat,
Button['Bnew']("New Equation", Evaluate('function' = "Show_Function"), background=turquoise),
HorizontalGlue(),
Button['BHint']("Hint", Evaluate('function' = "Hint"), background=lightorange),
Button("Quit", Shutdown(), background=pink)
],
BoxRow( background=wheat,
BoxColumn( border=true, background=wheat,
caption="Rotate the plot with the mouse.",
Plotter['myplot'](height=250, width=250)
),
BoxColumn( halign=none, inset=0, background=wheat,
BoxRow( halign=none, border=true, background=wheat,
caption = "Goal: Find the tangent plane to",
"f(x,y,z) =",
MathMLViewer[fMML]('value'=MathML[Export](" "), 'width'=200, 'height'=60),
"at (x,y,z) =",
MathMLViewer[pointMML]('value'=MathML[Export](" "), 'width'=100, 'height'=60)
),
BoxColumn( halign=none, border=true, inset=0, background=wheat,
caption = "Enter the partial derivatives of f:",
[ halign=none, background=wheat,
"df/dx = ",
TextField['fx']('width'=20, 'background'=turquoise),
HorizontalGlue(),
Button['Bfxck']("Check", Evaluate('function' = "Check_fx"), background=green),
TextField['fxck']('width'=6, editable=false, background=white),
Button['Bfxsh']("Show", Evaluate('function' = "Show_fx"), background=lightorange)
],
[ halign=none, background=wheat,
"df/dy = ",
TextField['fy']('width'=20, 'background'=turquoise),
HorizontalGlue(),
Button['Bfyck']("Check", Evaluate('function' = "Check_fy"), background=green),
TextField['fyck']('width'=6, editable=false, background=white),
Button['Bfysh']("Show", Evaluate('function' = "Show_fy"), background=lightorange)
],
[ halign=none, background=wheat,
"df/dz = ",
TextField['fz']('width'=20, 'background'=turquoise),
HorizontalGlue(),
Button['Bfzck']("Check", Evaluate('function' = "Check_fz"), background=green),
TextField['fzck']('width'=6, editable=false, background=white),
Button['Bfzsh']("Show", Evaluate('function' = "Show_fz"), background=lightorange)
]
),
BoxRow( halign=none, border=true, background=wheat,
caption = "Enter the tangent plane:",
TextField['ftan']('width'=26, 'background'=turquoise),
"= 0",
HorizontalGlue(),
Button['Bftanck']("Check", Evaluate('function' = "Check_ftan"), background=green),
TextField['ftanck']('width'=6, editable=false, background=white),
Button['Bftansh']("Show", Evaluate('function' = "Show_ftan"), background=lightorange)
)
)
), TextBox['reply']('width'=70, 'height'=2, 'editable'='false', background=white ),
[ halign=none, background="#DDFFFF", inset=0, spacing=0,
"Programmers: Carolyn Davidson and Lisa Cangelose",
HorizontalGlue(),
"\302\251 Copyright: P. Yasskin 2006"
]])):Maplets[Display]( Tangent_Line );