Permalink
Switch branches/tags
Nothing to show
Find file Copy path
Fetching contributors…
Cannot retrieve contributors at this time
751 lines (726 sloc) 33.4 KB
(* Content-type: application/vnd.wolfram.cdf.text *)
(*** Wolfram CDF File ***)
(* http://www.wolfram.com/cdf *)
(* CreatedBy='Mathematica 11.0' *)
(*************************************************************************)
(* *)
(* The Mathematica License under which this file was created prohibits *)
(* restricting third parties in receipt of this file from republishing *)
(* or redistributing it by any means, including but not limited to *)
(* rights management or terms of use, without the express consent of *)
(* Wolfram Research, Inc. For additional information concerning CDF *)
(* licensing and redistribution see: *)
(* *)
(* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *)
(* *)
(*************************************************************************)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 1064, 20]
NotebookDataLength[ 32319, 728]
NotebookOptionsPosition[ 32729, 719]
NotebookOutlinePosition[ 33106, 735]
CellTagsIndexPosition[ 33063, 732]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["Exponential functions", "Title"],
Cell["Creator: Johannes E. M. Mosig", "Text"],
Cell[TextData[{
"Click the graph to choose ",
Cell[BoxData[
FormBox["x", TraditionalForm]]],
", or drag the ",
Cell[BoxData[
FormBox[
StyleBox["base",
FontSlant->"Italic"], TraditionalForm]]],
" slider to change the basis. Click the \[OpenCurlyDoubleQuote]labels\
\[CloseCurlyDoubleQuote] checkbox to toggle some additional annotations."
}], "Text",
PageWidth->PaperWidth,
TextJustification->1.],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"DynamicModule", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"p0", "=",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}], ",",
RowBox[{"b", "=", "2."}], ",",
RowBox[{"showLbl", "=", "False"}]}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{"With", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x0", "=",
RowBox[{"Dynamic", "@",
RowBox[{"First", "@", "p0"}]}]}], ",",
RowBox[{"fofx", "=",
RowBox[{"Superscript", "[",
RowBox[{
RowBox[{"Dynamic", "@",
RowBox[{"Which", "[",
RowBox[{
RowBox[{"b", "\[Equal]", "\[ExponentialE]"}], ",", "\"\<e\>\"",
",",
RowBox[{"b", "\[Equal]", "1"}], ",", "1", ",",
RowBox[{"b", "\[Equal]", "2"}], ",", "2", ",",
RowBox[{"b", "\[Equal]", "3"}], ",", "3", ",", "True", ",",
RowBox[{"NumberForm", "[",
RowBox[{"b", ",",
RowBox[{"{",
RowBox[{"3", ",", "2"}], "}"}]}], "]"}]}], "]"}]}], ",",
"\"\<x\>\""}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{"Grid", "[",
RowBox[{
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"slider", " ", "for", " ", "base", " ", "selection"}], " ",
"*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Labeled", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"VerticalGauge", "[",
RowBox[{
RowBox[{"Dynamic", "[",
RowBox[{"b", ",", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"snap", " ", "to", " ", "certain", " ", "values"}],
" ", "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Which", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"#", "-", "\[ExponentialE]"}], "]"}], "<",
"0.1"}], ",",
RowBox[{"b", "=", "\[ExponentialE]"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"#", "-", "2"}], "]"}], "<", "0.1"}], ",",
RowBox[{"b", "=", "2."}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"#", "-", "1"}], "]"}], "<", "0.1"}], ",",
RowBox[{"b", "=", "1."}], ",", "\[IndentingNewLine]",
"True", ",",
RowBox[{"b", "=", "#"}]}], "\[IndentingNewLine]", "]"}],
"&"}], ",", "\[IndentingNewLine]", "Null", ",",
"\[IndentingNewLine]",
RowBox[{"TrackedSymbols", "\[RuleDelayed]",
RowBox[{"{", "b", "}"}]}]}], "\[IndentingNewLine]", "]"}],
",",
RowBox[{"{",
RowBox[{"0.01", ",", "3"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{"TicksStyle", "\[Rule]", "Large"}], ",",
"\[IndentingNewLine]",
RowBox[{"ImageSize", "\[Rule]", "80"}]}],
"\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]",
RowBox[{"Style", "[",
RowBox[{"\"\<base\>\"", ",", "Black", ",", "20"}], "]"}], ",",
"\[IndentingNewLine]", "Top"}], "\[IndentingNewLine]", "]"}],
",", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"plot", " ", "the", " ", "graph", " ", "and", " ", "tangent", " ",
"line"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{"LocatorPane", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Dynamic", "[",
RowBox[{"{", "p0", "}"}], "]"}], ",", "\[IndentingNewLine]",
RowBox[{"Dynamic", "@",
RowBox[{"Plot", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"f", "[",
RowBox[{"b", ",", "x"}], "]"}], ",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"-", "2"}], ",", "2"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"PlotStyle", "\[Rule]", "Black"}], ",",
"\[IndentingNewLine]",
RowBox[{"(*",
RowBox[{"PlotLabel", "\[Rule]",
RowBox[{"Dynamic", "@",
RowBox[{"Style", "[",
RowBox[{
RowBox[{
"\"\<f(x) = \!\(\*SuperscriptBox[\(b\), \(x\)]\), b = \
\>\"", "<>",
RowBox[{"If", "[",
RowBox[{
RowBox[{"b", "\[Equal]", "\[ExponentialE]"}], ",",
"\"\<e \[TildeTilde] 2.718\>\"", ",",
RowBox[{"ToString", "[",
RowBox[{"Round", "[",
RowBox[{"b", ",", "0.01"}], "]"}], "]"}]}], "]"}]}], ",",
"Black", ",", "20", ",", "Italic"}], "]"}]}]}], "*)"}],
"\[IndentingNewLine]",
RowBox[{"PlotLabel", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Row", "[",
RowBox[{"{",
RowBox[{"\"\<f(x) = \>\"", ",", "fofx"}], "}"}], "]"}],
",", "Black", ",", "20", ",", "Italic"}], "]"}]}], ",",
"\[IndentingNewLine]",
RowBox[{"AxesOrigin", "\[Rule]",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}], ",",
"\[IndentingNewLine]",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{"Thick", ",",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{
{GrayLevel[0], RectangleBox[{0, 0}]},
{GrayLevel[0], RectangleBox[{1, -1}]},
{RGBColor[0.790588, 0.201176, 0.],
RectangleBox[{0, -1}, {2, 1}]}},
AspectRatio->1,
Frame->True,
FrameStyle->RGBColor[
0.5270586666666667, 0.13411733333333334`, 0.],
FrameTicks->None,
ImageSize->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}],
PlotRangePadding->None],
"RGBColor[0.790588, 0.201176, 0.]"],
Appearance->None,
BaseStyle->{},
BaselinePosition->Baseline,
ButtonFunction:>With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0.790588, 0.201176, 0.];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]],
DefaultBaseStyle->{},
Evaluator->Automatic,
Method->"Preemptive"],
RGBColor[0.790588, 0.201176, 0.],
Editable->False,
Selectable->False], ",",
RowBox[{"PointSize", "\[Rule]", "Large"}], ",",
"\[IndentingNewLine]",
RowBox[{"Point", "[",
RowBox[{"{",
RowBox[{"{",
RowBox[{"x0", ",",
RowBox[{"f", "[",
RowBox[{"b", ",", "x0"}], "]"}]}], "}"}], "}"}], "]"}],
",", "\[IndentingNewLine]",
RowBox[{"InfiniteLine", "[",
RowBox[{
RowBox[{"{",
RowBox[{"x0", ",",
RowBox[{"f", "[",
RowBox[{"b", ",", "x0"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",",
RowBox[{
RowBox[{
RowBox[{"Derivative", "[",
RowBox[{"0", ",", "1"}], "]"}], "[", "f", "]"}], "[",
RowBox[{"b", ",", "x0"}], "]"}]}], "}"}]}], "]"}], ",",
"\[IndentingNewLine]",
InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{
{GrayLevel[0], RectangleBox[{0, 0}]},
{GrayLevel[0], RectangleBox[{1, -1}]},
{RGBColor[0.192157, 0.388235, 0.807843],
RectangleBox[{0, -1}, {2, 1}]}},
AspectRatio->1,
Frame->True,
FrameStyle->RGBColor[
0.12810466666666667`, 0.25882333333333335`, 0.538562],
FrameTicks->None,
ImageSize->
Dynamic[{
Automatic,
1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
Magnification])}],
PlotRangePadding->None],
"RGBColor[0.192157, 0.388235, 0.807843]"],
Appearance->None,
BaseStyle->{},
BaselinePosition->Baseline,
ButtonFunction:>With[{Typeset`box$ = EvaluationBox[]},
If[
Not[
AbsoluteCurrentValue["Deployed"]],
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
RGBColor[0.192157, 0.388235, 0.807843];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
FrontEndResource["RGBColorValueSelector"], {
0, {Left, Bottom}}, {Left, Top},
"ClosingActions" -> {
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]],
DefaultBaseStyle->{},
Evaluator->Automatic,
Method->"Preemptive"],
RGBColor[0.192157, 0.388235, 0.807843],
Editable->False,
Selectable->False], ",", "\[IndentingNewLine]",
RowBox[{"If", "[",
RowBox[{
RowBox[{"b", "\[NotEqual]", "1"}], ",",
RowBox[{"Line", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"x0", ",",
RowBox[{"f", "[",
RowBox[{"b", ",", "x0"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x0", "-",
RowBox[{"1", "/",
RowBox[{"Log", "[", "b", "]"}]}]}], ",", "0"}], "}"}]}],
"}"}], "]"}], ",",
RowBox[{"{", "}"}]}], "]"}], ",", "\[IndentingNewLine]",
RowBox[{"If", "[",
RowBox[{"showLbl", ",", "\[IndentingNewLine]",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{"Black", ",", "\[IndentingNewLine]",
RowBox[{"Text", "[",
RowBox[{
RowBox[{"Style", "[",
RowBox[{"fofx", ",", "Large", ",", "Black"}], "]"}], ",",
RowBox[{"{",
RowBox[{"x0", ",",
RowBox[{
RowBox[{"f", "[",
RowBox[{"b", ",", "x0"}], "]"}], "/", "2"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1.4"}], ",", "0"}], "}"}]}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"Text", "[",
RowBox[{
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Row", "[",
RowBox[{"{",
RowBox[{
"\"\<slope = \>\"", ",", "fofx", ",",
"\"\<\[CenterDot]\>\"", ",",
RowBox[{"N", "[",
RowBox[{"Log", "[", "b", "]"}], "]"}]}], "}"}], "]"}],
",", "Large", ",", "Black"}], "]"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x0", "+", "0.3"}], ",",
RowBox[{"f", "[",
RowBox[{"b", ",",
RowBox[{"x0", "+", "0.3"}]}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1.4"}], ",", "0"}], "}"}]}], "]"}]}],
"\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]",
RowBox[{"{", "}"}]}], "\[IndentingNewLine]", "]"}]}],
"\[IndentingNewLine]", "}"}]}], ",", "\[IndentingNewLine]",
RowBox[{"ImageSize", "\[Rule]", "Large"}], ",",
"\[IndentingNewLine]",
RowBox[{"PlotRangePadding", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}]}], "}"}]}]}],
"\[IndentingNewLine]", "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{"Appearance", "\[Rule]", "None"}]}],
"\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Labeled", "[",
RowBox[{
RowBox[{"Checkbox", "[",
RowBox[{"Dynamic", "@", "showLbl"}], "]"}], ",",
"\"\<labels\>\"", ",", "Right"}], "]"}], ",",
"\[IndentingNewLine]", "SpanFromAbove"}], "\[IndentingNewLine]",
"}"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]",
RowBox[{"ItemSize", "\[Rule]", "Full"}]}], "\[IndentingNewLine]",
"]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]",
RowBox[{"Initialization", "\[RuleDelayed]",
RowBox[{"(", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{
"bug", " ", "fix", " ", "for", " ", "CDF", " ", "player", " ", "11.2"}],
" ", "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"Unprotect", "[", "Point", "]"}], ";", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Point", "[",
RowBox[{"{",
RowBox[{"l", ":",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"_", ",", "_"}], "}"}], ".."}], "}"}]}], "}"}], "]"}], ":=",
RowBox[{"Point", "[", "l", "]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"Protect", "[", "Point", "]"}], ";", "\[IndentingNewLine]",
RowBox[{"(*", " ",
RowBox[{"define", " ", "f"}], " ", "*)"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"f", "[",
RowBox[{"b_", ",", "x_"}], "]"}], ":=",
SuperscriptBox["b", "x"]}]}], "\[IndentingNewLine]", ")"}]}], ",",
"\[IndentingNewLine]",
RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "\[IndentingNewLine]",
"]"}]], "Input"],
Cell[BoxData[
DynamicModuleBox[{$CellContext`p0$$ = {0.6499999999999999,
2.935}, $CellContext`b$$ = 2., $CellContext`showLbl$$ = False},
TagBox[GridBox[{
{
TemplateBox[{DynamicModuleBox[{System`GaugesDump`height$$ = Dynamic[
Charting`barValHeight[$CellContext`b$$, {Identity, Identity}, {
0.01, 3}, {{0, 0}, {0, 1}}, Rational[1, 2] Pi]],
System`GaugesDump`pt$$ = {0., 0.6655518394648829}},
LocatorPaneBox[
Dynamic[
Charting`barValueToPoint[$CellContext`b$$, {Identity, Identity}, {
0.01, 3}, {{0, 0}, {0, 1}}, Rational[1, 2] Pi], {
None, (System`GaugesDump`height$$ =
Charting`barPointtoValue[#, {Identity, Identity}, {0.01, 3}, {{0,
0}, {0, 1}}, Rational[1, 2] Pi]; $CellContext`b$$ = (
Part[{None, Which[
Abs[# - E] < 0.1, $CellContext`b$$ = E, Abs[# - 2] <
0.1, $CellContext`b$$ = 2., Abs[# - 1] <
0.1, $CellContext`b$$ = 1., True, $CellContext`b$$ = #]& ,
Null, TrackedSymbols :> {$CellContext`b$$}, None}, 2][
System`GaugesDump`height$$, #2]; $CellContext`b$$);
System`GaugesDump`pt$$ =
Charting`barValueToPoint[$CellContext`b$$, {
Identity, Identity}, {0.01, 3}, {{0, 0}, {0, 1}},
Rational[1, 2] Pi]; Null)& , Null}, {}],
GraphicsBox[{{}, {
Opacity[0],
PointBox[{{-0.15, -0.1}, {0.15, 1.1}}]},
GeometricTransformationBox[{{}}, {{{0, -1}, {1, 0}}, {0, 0}}], {{
Antialiasing -> False,
StyleBox[
LineBox[{{0., 0.}, {0., 1.}}], {}, StripOnInput -> False,
StripOnInput -> False],
StyleBox[
StyleBox[{{
StyleBox[
StyleBox[
LineBox[{{{0., 0.3311036789297659},
Scaled[{-0.06, 0.}, {0., 0.3311036789297659}]}, {{0.,
0.6655518394648829},
Scaled[{-0.06, 0.}, {0., 0.6655518394648829}]}, {{0., 1.},
Scaled[{-0.06, 0.}, {0., 1.}]}}], Large, StripOnInput ->
False, StripOnInput -> False],
Directive[
CapForm["Butt"],
AbsoluteThickness[1],
GrayLevel[0.5]], StripOnInput -> False, StripOnInput ->
False],
StyleBox[
StyleBox[
LineBox[{{{0., 0.0802675585284281},
Scaled[{-0.04, 0.}, {0., 0.0802675585284281}]}, {{0.,
0.16387959866220736`},
Scaled[{-0.04, 0.}, {0., 0.16387959866220736`}]}, {{0.,
0.24749163879598662`},
Scaled[{-0.04, 0.}, {0., 0.24749163879598662`}]}, {{0.,
0.41471571906354515`},
Scaled[{-0.04, 0.}, {0., 0.41471571906354515`}]}, {{0.,
0.4983277591973244},
Scaled[{-0.04, 0.}, {0., 0.4983277591973244}]}, {{0.,
0.5819397993311036},
Scaled[{-0.04, 0.}, {0., 0.5819397993311036}]}, {{0.,
0.7491638795986623},
Scaled[{-0.04, 0.}, {0., 0.7491638795986623}]}, {{0.,
0.8327759197324416},
Scaled[{-0.04, 0.}, {0., 0.8327759197324416}]}, {{0.,
0.9163879598662208},
Scaled[{-0.04, 0.}, {0., 0.9163879598662208}]}}], Large,
StripOnInput -> False, StripOnInput -> False],
Directive[
CapForm["Butt"],
AbsoluteThickness[0.5],
GrayLevel[0.5]], StripOnInput -> False, StripOnInput ->
False]},
StyleBox[
StyleBox[{{
StyleBox[{
InsetBox[
BoxData[
FormBox["1", TraditionalForm]],
Offset[{3., 0.}, {0., 0.3311036789297659}],
ImageScaled[{0, 0.5}], Automatic, {1, 0}],
InsetBox[
BoxData[
FormBox["2", TraditionalForm]],
Offset[{3., 0.}, {0., 0.6655518394648829}],
ImageScaled[{0, 0.5}], Automatic, {1, 0}],
InsetBox[
BoxData[
FormBox["3", TraditionalForm]],
Offset[{3., 0.}, {0., 1.}],
ImageScaled[{0, 0.5}], Automatic, {1, 0}]},
Large, {{}, {}}, StripOnInput -> False, StripOnInput ->
False],
StyleBox[{{}, {}, {}, {}, {}, {}, {}, {}, {}},
Large, {{}, {}}, StripOnInput -> False, StripOnInput ->
False]}, {}}, {Large, Large}, StripOnInput -> False,
StripOnInput -> False],
Directive[
AbsoluteThickness[1],
GrayLevel[0.5]], StripOnInput -> False, StripOnInput ->
False]}, {
Directive[
CapForm["Butt"],
AbsoluteThickness[1],
GrayLevel[0.5]],
Directive[
CapForm["Butt"],
AbsoluteThickness[0.5],
GrayLevel[0.5]]}, StripOnInput -> False, StripOnInput ->
False], {}, StripOnInput -> False, StripOnInput ->
False]}, {}}, {}, {
Directive[
RGBColor[0.73, 0.24506099999999992`, 0.1971]],
GeometricTransformationBox[{{},
Directive[
RGBColor[0.73, 0.24506099999999992`, 0.1971]], {},
"MarkerRotation" -> Rational[1, 2] Pi,
TagBox[
TooltipBox[
PolygonBox[{{0.5, 0.5}, {-0.5, 0.5}, {0., -0.5}}],
DynamicBox[
ToBoxes[$CellContext`b$$, StandardForm]]], Annotation[#,
Dynamic[$CellContext`b$$], "Tooltip"]& ]}, {{{0., -0.075}, {
0.075,
0.}}, {-0.0375, 1. (0. + 0.33444816053511706` (-0.01 + 1. If[
Dynamic[
MatchQ[$CellContext`b$$,
PatternTest[
Blank[], Charting`realNumericQ]]],
Dynamic[
Clip[$CellContext`b$$,
Sort[
N[{0.01, 3.}], Less]]], 0.01]))}}]}, {},
GeometricTransformationBox[{}, {{{0, -1}, {1, 0}}, {0, 0}}]}, {
AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False,
AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {},
Background -> None, BaselinePosition -> Automatic,
BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable ->
Automatic, CoordinatesToolOptions -> Automatic, DisplayFunction ->
Identity, Epilog -> {}, FormatType -> TraditionalForm, Frame ->
False, FrameLabel -> None, FrameStyle -> {}, FrameTicks ->
Automatic, FrameTicksStyle -> {}, GridLines -> None,
GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All,
ImageSize -> 80, ImageSizeRaw -> Automatic, LabelStyle -> {},
Method -> {
"DefaultBoundaryStyle" -> Automatic, "DefaultPlotStyle" ->
Automatic}, PlotLabel -> None, PlotRange -> All,
PlotRangeClipping -> False, PlotRangePadding -> Automatic,
PlotRegion -> Automatic, PreserveImageOptions -> Automatic,
Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle ->
Large, Axes -> False, Method -> Automatic}], Appearance -> None,
Enabled -> Automatic], DynamicModuleValues :> {}],StyleBox[
"\"base\"",
GrayLevel[0], 20, StripOnInput -> False]},
"Labeled",
DisplayFunction->(GridBox[{{
ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}, {
TagBox[
ItemBox[
PaneBox[
TagBox[#, "SkipImageSizeLevel"],
Alignment -> {Center, Baseline}, BaselinePosition -> Baseline],
DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}},
GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}},
AutoDelete -> False,
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
BaselinePosition -> {2, 1}]& ),
InterpretationFunction->(RowBox[{"Labeled", "[",
RowBox[{#, ",", #2, ",", "Top"}], "]"}]& )],
LocatorPaneBox[Dynamic[{$CellContext`p0$$}],
DynamicBox[ToBoxes[
Plot[
$CellContext`f[$CellContext`b$$, $CellContext`x], {$CellContext`x, \
-2, 2}, PlotStyle -> Black, PlotLabel -> Style[
Row[{"f(x) = ",
Superscript[
Dynamic[
Which[$CellContext`b$$ == E, "e", $CellContext`b$$ == 1,
1, $CellContext`b$$ == 2, 2, $CellContext`b$$ == 3, 3, True,
NumberForm[$CellContext`b$$, {3, 2}]]], "x"]}], Black, 20,
Italic], AxesOrigin -> {0, 0}, Epilog -> {Thick,
RGBColor[0.790588, 0.201176, 0.], PointSize -> Large,
Point[{{
Dynamic[
First[$CellContext`p0$$]],
$CellContext`f[$CellContext`b$$,
Dynamic[
First[$CellContext`p0$$]]]}}],
InfiniteLine[{
Dynamic[
First[$CellContext`p0$$]],
$CellContext`f[$CellContext`b$$,
Dynamic[
First[$CellContext`p0$$]]]}, {1,
Derivative[0, 1][$CellContext`f][$CellContext`b$$,
Dynamic[
First[$CellContext`p0$$]]]}],
RGBColor[0.192157, 0.388235, 0.807843],
If[$CellContext`b$$ != 1,
Line[{{
Dynamic[
First[$CellContext`p0$$]],
$CellContext`f[$CellContext`b$$,
Dynamic[
First[$CellContext`p0$$]]]}, {
Dynamic[
First[$CellContext`p0$$]], 0}, {Dynamic[
First[$CellContext`p0$$]] - 1/Log[$CellContext`b$$],
0}}], {}],
If[$CellContext`showLbl$$, {Black,
Text[
Style[
Superscript[
Dynamic[
Which[$CellContext`b$$ == E, "e", $CellContext`b$$ == 1,
1, $CellContext`b$$ == 2, 2, $CellContext`b$$ == 3, 3,
True,
NumberForm[$CellContext`b$$, {3, 2}]]], "x"], Large,
Black], {
Dynamic[
First[$CellContext`p0$$]], $CellContext`f[$CellContext`b$$,
Dynamic[
First[$CellContext`p0$$]]]/2}, {-1.4, 0}],
Text[
Style[
Row[{"slope = ",
Superscript[
Dynamic[
Which[$CellContext`b$$ == E, "e", $CellContext`b$$ == 1,
1, $CellContext`b$$ == 2, 2, $CellContext`b$$ == 3, 3,
True,
NumberForm[$CellContext`b$$, {3, 2}]]], "x"],
"\[CenterDot]",
N[
Log[$CellContext`b$$]]}], Large, Black], {Dynamic[
First[$CellContext`p0$$]] + 0.3,
$CellContext`f[$CellContext`b$$, Dynamic[
First[$CellContext`p0$$]] + 0.3]}, {-1.4, 0}]}, {}]},
ImageSize -> Large, PlotRangePadding -> {{0, 2}, {0, 0}}],
StandardForm],
ImageSizeCache->{576., {196., 201.}}],
Appearance->None]},
{
TemplateBox[{CheckboxBox[
Dynamic[$CellContext`showLbl$$]],"\"labels\""},
"Labeled",
DisplayFunction->(GridBox[{{
TagBox[
ItemBox[
PaneBox[
TagBox[#, "SkipImageSizeLevel"],
Alignment -> {Center, Baseline}, BaselinePosition -> Baseline],
DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"],
ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}},
GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}},
AutoDelete -> False,
GridBoxItemSize -> {
"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
BaselinePosition -> {1, 1}]& ),
InterpretationFunction->(RowBox[{"Labeled", "[",
RowBox[{#, ",", #2, ",", "Right"}], "]"}]& )], "\[SpanFromAbove]"}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{All}}, "Rows" -> {{All}}}],
"Grid"],
DynamicModuleValues:>{},
Initialization:>({$CellContext`f[
Pattern[$CellContext`x,
Blank[]]] := E^$CellContext`x, $CellContext`f[
Pattern[$CellContext`b,
Blank[]],
Pattern[$CellContext`x,
Blank[]]] := $CellContext`b^$CellContext`x,
Attributes[Superscript] = {NHoldRest, ReadProtected},
Attributes[Derivative] = {NHoldAll, ReadProtected}}; (Unprotect[Point];
Point[{
Pattern[$CellContext`l, {
Repeated[{
Blank[],
Blank[]}]}]}] := Point[$CellContext`l];
Protect[Point]; $CellContext`f[
Pattern[$CellContext`b,
Blank[]],
Pattern[$CellContext`x,
Blank[]]] := $CellContext`b^$CellContext`x))]], "Output"]
}, {2}]]
}, Open ]]
},
WindowSize->{873, 710},
WindowMargins->{{122, Automatic}, {Automatic, 24}},
TrackCellChangeTimes->False,
FrontEndVersion->"11.0 for Microsoft Windows (64-bit) (September 21, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[1486, 35, 38, 0, 101, "Title"],
Cell[1527, 37, 45, 0, 30, "Text"],
Cell[1575, 39, 413, 13, 68, "Text"],
Cell[CellGroupData[{
Cell[2013, 56, 16811, 363, 1361, "Input"],
Cell[18827, 421, 13877, 294, 420, "Output"]
}, {2}]]
}, Open ]]
}
]
*)
(* NotebookSignature NvDw1FTzk9#lNCKnxP3slITA *)