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How to modify the code to make the function image clear?

Lee Tao

Posted 1 year ago

How to modify the code so that the abscissa and ordinate of the original function and derivative function are adaptive in the same coordinate system so that the displayed image size is appropriate and the form of the function image can be felt as a whole ClearAll@f; f[x_] := Log[x]/-x^2 Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}]; orders = Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // ToString, {n, 0, nMax, 1}]; labels = MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, functions}];]; Plot[functions, {x, 0, 1}, PlotLabels -> labels, PlotRange -> All, ImageSize -> 700, AspectRatio -> 1, PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1, PopupMenu}]

How to modify the code so that the abscissa and ordinate of the original function and derivative function are adaptive in the same coordinate system so that the displayed image size is appropriate and the form of the function image can be felt as a whole

ClearAll@f;

f[x_] := Log[x]/-x^2

Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}];
  orders = 
   Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // 
     ToString, {n, 0, nMax, 1}];
  labels = 
   MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, 
     functions}];];
 Plot[functions, {x, 0, 1}, PlotLabels -> labels, PlotRange -> All, 
  ImageSize -> 700, AspectRatio -> 1, 
  PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1,
   PopupMenu}]

POSTED BY: Lee Tao

5 Replies

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Rohit Namjoshi

Posted 1 year ago

The problem is that the functions depend inversely on `x` so they diverge as `x -> 0`. Try removing `PlotRange -> All`.

POSTED BY: Rohit Namjoshi

Lee Tao

Posted 1 year ago

The previous effect is like this, which obviously does not meet the requirements

POSTED BY: Lee Tao

Lee Tao

Posted 1 year ago

ClearAll@f; f[x_] := Log[x]/-x^2 Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}]; orders = Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // ToString, {n, 0, nMax, 1}]; labels = MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, functions}];]; Plot[functions, {x, 0, 13}, PlotLabels -> labels, ImageSize -> 700, AspectRatio -> 1, PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1, PopupMenu}]

ClearAll@f;

f[x_] := Log[x]/-x^2
Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}];
  orders = 
   Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // 
     ToString, {n, 0, nMax, 1}];
  labels = 
   MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, 
     functions}];];
 Plot[functions, {x, 0, 13}, PlotLabels -> labels, ImageSize -> 700, 
  AspectRatio -> 1, 
  PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1,
   PopupMenu}]

POSTED BY: Lee Tao

Lee Tao

Posted 1 year ago

POSTED BY: Lee Tao

Lee Tao

Posted 1 year ago

Set to equal horizontal and vertical coordinates ClearAll@f; f[x_] := x Log[x] Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}]; orders = Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // ToString, {n, 0, nMax, 1}]; labels = MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, functions}];]; Plot[functions, {x, 0, 5}, PlotLabels -> labels, ImageSize -> 700, AspectRatio -> Automatic, PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1, PopupMenu}]

Set to equal horizontal and vertical coordinates

ClearAll@f;

f[x_] := x Log[x]
Manipulate[Refresh[functions = Table[D[f[x], {x, n}], {n, 0, nMax, 1}];
  orders = 
   Table[D[f[x], {x, n}] // Inactivate // TraditionalForm // 
     ToString, {n, 0, nMax, 1}];
  labels = 
   MapThread[#1 <> " = " <> ToString[#2, TraditionalForm] &, {orders, 
     functions}];];
 Plot[functions, {x, 0, 5}, PlotLabels -> labels, ImageSize -> 700, 
  AspectRatio -> Automatic, 
  PlotLabel -> Row[{"f(x) = ", f[x]}]], {{nMax, 1, "Order"}, 1, 10, 1,
   PopupMenu}]

POSTED BY: Lee Tao

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