restart:
with(Maplets[Elements]):with(Maplets[Tools]):
StartEngine();
randomize():
great := [
" Correct. ",
" YES! ",
" Perfect. ",
" Awesome! ",
" Excellent! ",
" Way to GO!",
" Now that's how you do it!",
" I couldn't have done it better! ",
" Ding Ding Ding, we have a winner. "
]:
randgreat := rand(1..nops(great)):
nextquest := [
"Try another one.",
"Give it another shot.",
"Can you do that again?",
"Approximate another point."
]:
randnext := rand(1..nops(nextquest)):
sorry := [
" Not really what I was looking for. ",
" Nope. ",
" Sorry, That's incorrect. ",
" Ooooh...so close. ",
" Oops. ",
" Wrong Wrong Wrong. You have it all WRONG. "
]:
randsorry := rand(1..nops(sorry)):
tryagain := [
"Try the hint.",
"Guess again.",
"They say the third times the charm. Please try again.",
"Try again.",
"Please try again."
]:
randtry := rand(1..nops(tryagain)):
showit := [
" OK now try it yourself.",
" I know how you work- you click SHOW IT so I have to do all the work! How about you try it yourself!?",
" Now try using your own mind for a change to solve the problem.",
" Do you see how it's done now? Okay now you try it.",
" That was practice. Now it's your turn."
]:
randshow := rand(1..nops(showit)):
 
i:=0:
i:=i+1:
funcs[i]:=1/x:
i:=i+1:
funcs[i]:=x^2:
i:=i+1:
funcs[i]:=1/x^2:
i:=i+1:
funcs[i]:=x^2+3*x+5:
i:=i+1:
funcs[i]:=x+x^2/3:
i:=i+1:
funcs[i]:=x^3-2*x+5:
i:=i+1:
funcs[i]:=4*x-x^3:
i:=i+1:
funcs[i]:=7*x-x^2+2/4:
i:='i':
randfunc := rand(1..8):
 
Show_Function := proc()
  local p1;
  global randfunc, whichfunc, funcs, func, A, randpt, As, randpts, whichpoint, x, a, funca, funcp, funcpa, functan, functana;
  whichfunc := randfunc();
  func := funcs[whichfunc];
  funca := eval(func, x=2);
  funcp := diff(func,x);
  funcpa := simplify(eval(funcp, x=2));
  functan := funca + funcpa * (x-2);
  functana := funca + funcpa * (2.1-2);
  Set('fMML' = func):
  Set('fa' = ""):
  Set('fp' = ""):
  Set('fpa' = ""):
  Set('ftan' = ""):
  Set('ftana' =""):
  Set('fack' = "", 'fack'(background)=white, 'fack'(foreground) = black):
  Set('fpck' = "", 'fpck'(background)=white, 'fpck'(foreground) = black):
  Set('fpack' = "", 'fpack'(background)=white, 'fpack'(foreground) = black):
  Set('ftanck' = "", 'ftanck'(background)=white, 'ftanck'(foreground) = black):
  Set('ftanack' = "", 'ftanack'(background)=white, 'ftanack'(foreground) = black):
  Set('reply' = "", 'reply'(background)=white, 'reply'(foreground) = black):

  Set('Bfack'(enabled)=true, 'Bfack'(background)=turquoise);
  Set('Bfash'(enabled)=true, 'Bfash'(background)=turquoise);
  Set('Bfpck'(enabled)=true, 'Bfpck'(background)=turquoise);
  Set('Bfpsh'(enabled)=true, 'Bfpsh'(background)=turquoise);
  Set('Bfpack'(enabled)=true, 'Bfpack'(background)=turquoise);
  Set('Bfpash'(enabled)=true, 'Bfpash'(background)=turquoise);
  Set('Bftanck'(enabled)=true, 'Bftanck'(background)=turquoise);
  Set('Bftanack'(enabled)=true, 'Bftanack'(background)=turquoise);
  Set('Bftanash'(enabled)=true, 'Bftanash'(background)=turquoise);
  Set('Bftansh'(enabled)=true, 'Bftansh'(background)=turquoise);

end proc:
 
Check_fa := proc()
  local user_fa;
  global funca, x;
  user_fa := Get('fa'::algebraic, corrections=true, update=true):
  if simplify(normal(funca - user_fa))<> 0
    then
    Set('fack' = "incorrect", 'fack'(background)=red, 'fack'(foreground) = white):
    Set('reply' = cat(sorry[randsorry()], tryagain[randtry()]), 'reply'(background)=red, 'reply'(foreground) = white):
    else
    Set('fack' = " correct ", 'fack'(background)=green, 'fack'(foreground) = black):
    Set('reply' = cat(great[randgreat()]), 'reply'(background)=green, 'reply'(foreground) = black):
  end if;
end proc:
Show_fa := proc()
  global funca, x;
  Set('fa' = funca):
  Set('fack' = " ", 'fack'(background)=white, 'fack'(foreground) = black):
  Set('reply' = showit[randshow()], 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:
 
Check_fp := proc()
  local user_fp;
  global funcp, x;
  user_fp := Get('fp'::algebraic, corrections=true, update=true):
  if simplify(normal(funcp - user_fp))<> 0
    then
    Set('fpck' = "incorrect", 'fpck'(background)=red, 'fpck'(foreground) = white):
    Set('reply' = cat(sorry[randsorry()], tryagain[randtry()]), 'reply'(background)=red, 'reply'(foreground) = white):
    else
    Set('fpck' = " correct ", 'fpck'(background)=green, 'fpck'(foreground) = black):
    Set('reply' = cat(great[randgreat()]), 'reply'(background)=green, 'reply'(foreground) = black):
  end if;
end proc:
Show_fp := proc()
  global funcp, x;
  Set('fp' = funcp):
  Set('fpck' = " ", 'fpck'(background)=white, 'fpck'(foreground) = black):
  Set('reply' = showit[randshow()], 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:
 
Check_fpa := proc()
  local user_fpa;
  global funcpa, x;
  user_fpa := Get('fpa'::algebraic, corrections=true, update=true):
  if simplify(normal(funcpa - user_fpa))<> 0
    then
    Set('fpack' = "incorrect", 'fpack'(background)=red, 'fpack'(foreground) = white):
    Set('reply' = cat(sorry[randsorry()], tryagain[randtry()]), 'reply'(background)=red, 'reply'(foreground) = white):
    else
    Set('fpack' = " correct ", 'fpack'(background)=green, 'fpack'(foreground) = black):
    Set('reply' = cat(great[randgreat()]), 'reply'(background)=green, 'reply'(foreground) = black):
  end if;
end proc:
Show_fpa := proc()
  global funcpa, x;
  Set('fpa' = funcpa):
  Set('fpack' = " ", 'fpack'(background)=white, 'fpack'(foreground) = black):
  Set('reply' = showit[randshow()], 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:
 
Check_ftan := proc()
  local user_ftan;
  global functan, x;
  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()]), 'reply'(background)=green, 'reply'(foreground) = black):
  end if;
end proc:
Show_ftan := proc()
  global funcpa, x;
  Set('ftan' = functan):
  Set('ftanck' = " ", 'ftanck'(background)=white, 'ftanck'(foreground) = black):
  Set('reply' = showit[randshow()], 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:

Check_ftana := proc()
  local user_ftana;
  global functana, x;
  user_ftana := Get('ftana'::algebraic, corrections=true, update=true):
  if simplify(normal(functana - user_ftana))<> 0
    then
    Set('ftanack' = "incorrect", 'ftanack'(background)=red, 'ftanack'(foreground) = white):
    Set('reply' = cat(sorry[randsorry()], tryagain[randtry()]), 'reply'(background)=red, 'reply'(foreground) = white):
    else
    Set('ftanack' = " correct ", 'ftanack'(background)=green, 'ftanack'(foreground) = black):
    Set('reply' = cat(great[randgreat()], nextquest[randnext()]), 'reply'(background)=green, 'reply'(foreground) = black):
  end if;
end proc:
Show_ftana := proc()
  global funcpa, x;
  Set('ftana' = functana):
  Set('ftanack' = " ", 'ftanack'(background)=white, 'ftanack'(foreground) = black):
  Set('reply' = showit[randshow()], 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:
 
Hint := proc()
global a;
Set('reply' = cat("Use the function L(x) = f(a) + f'(a) (x-a) to compute the linear approximation."), 'reply'(background)=turquoise, 'reply'(foreground) = black):
end proc:

LinearApproximation := Maplet(onstartup = RunWindow(MAIN), Font[helv10]("helvetica",10),
Window[MAIN]( 'title'="Finding Linear Approximations", 'defaultbutton'='BHint', 
[ halign=none, background=wheat,
  [ background=wheat,
    Button['Bnew']("New Function", Evaluate('function' = "Show_Function"), background=turquoise),
    HorizontalGlue(),
    Button['BHint']("Hint", Evaluate('function' = "Hint"), background=turquoise),
    Button("Quit", Shutdown(), background=turquoise)
  ],
  BoxColumn( halign=none, border=true, inset=0, background=wheat,
          caption = "Goal:",
    [background=wheat,
    "Find the linear approximation of   f (x) =",
    MathMLViewer[fMML]('value'=MathML[Export](" "), 'width'=100, 'height'=60),
    "at the point   x = 2",
    HorizontalGlue()
    ],
    [background=wheat,
    "Use it to approximate   f (2.1).",
    HorizontalGlue()
    ]
  ),
  BoxColumn( halign=none, border=true, inset=0, background=wheat,
    caption = "Let's see what you can do:",
    [ background=wheat,
      " f(2) = ",
      TextField['fa']('width'=20, 'background'=pink),
      HorizontalGlue(),
      Button['Bfack']("Check", Evaluate('function' = "Check_fa"), background=wheat, enabled=false),
      TextField['fack']('width'=6, editable=false, background=white),
      Button['Bfash']("Show", Evaluate('function' = "Show_fa"), background=wheat, enabled=false)
    ],
    [ background=wheat,
      " f '(x) = ",
      TextField['fp']('width'=20, 'background'=pink),
      HorizontalGlue(),
      Button['Bfpck']("Check", Evaluate('function' = "Check_fp"), background=wheat, enabled=false),
      TextField['fpck']('width'=6, editable=false, background=white),
      Button['Bfpsh']("Show", Evaluate('function' = "Show_fp"), background=wheat, enabled=false)
    ],
    [ background=wheat,
      " f '(2) = ",
      TextField['fpa']('width'=20, 'background'=pink),
      HorizontalGlue(),
      Button['Bfpack']("Check", Evaluate('function' = "Check_fpa"), background=wheat, enabled=false),
      TextField['fpack']('width'=6, editable=false, background=white),
      Button['Bfpash']("Show", Evaluate('function' = "Show_fpa"), background=wheat, enabled=false)
    ],
    [ background=wheat,
      " L(x) = ",
      TextField['ftan']('width'=20, 'background'=pink),
      HorizontalGlue(),
      Button['Bftanck']("Check", Evaluate('function' = "Check_ftan"), background=wheat, enabled=false),
      TextField['ftanck']('width'=6, editable=false, background=white),
      Button['Bftansh']("Show", Evaluate('function' = "Show_ftan"), background=wheat, enabled=false)
    ]
  ),
  BoxRow( border=true, inset=0, background=wheat,
    caption = "Approximate:",
    "  f(2.1) ~",
    TextField['ftana']('width'=26, 'background'=pink),
    HorizontalGlue(),
    Button['Bftanack']("Check", Evaluate('function' = "Check_ftana"), background=wheat, enabled=false),
    TextField['ftanack']('width'=6, editable=false, background=white),
    Button['Bftanash']("Show", Evaluate('function' = "Show_ftana"), background=wheat, enabled=false),
    ""
  ),
  TextBox['reply']('width'=70, 'height'=2, 'editable'='false', background=white ),
  BoxRow('background'=pink, 'inset'=0, 'spacing'=0,
    Label("Copyright November 2005", 'font'=helv10),
    HorizontalGlue(),
    Label("Project By:Jessica Bailey", 'font'=helv10),
    HorizontalGlue(),
    Label("Yasskin Math151-202", 'font'=helv10)
  )
]),
ButtonGroup['BG1']()
):
Maplets[Display]( LinearApproximation );