(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 10.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 46780, 1250]
NotebookOptionsPosition[ 45777, 1211]
NotebookOutlinePosition[ 46113, 1226]
CellTagsIndexPosition[ 46070, 1223]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{
RowBox[{"f", "[", "x_", "]"}], " ", ":=", " ",
RowBox[{"Cos", "[", "x", "]"}]}]], "Input",
CellChangeTimes->{{3.683213270757375*^9, 3.683213279924851*^9}, {
3.683213869842869*^9, 3.683213902127639*^9}, {3.683214036747176*^9,
3.683214048317216*^9}, {3.6832140786082277`*^9, 3.683214084450881*^9}, {
3.68321414613465*^9, 3.683214146652562*^9}, {3.683214367655723*^9,
3.683214369708709*^9}, {3.6832144130675373`*^9, 3.6832144253845243`*^9}, {
3.68321446416663*^9, 3.683214475096218*^9}, 3.683214546371379*^9, {
3.6832146032640047`*^9, 3.683214605860536*^9}, {3.683214663185094*^9,
3.683214707622348*^9}, {3.683214756018661*^9, 3.683214793562089*^9}, {
3.683214828234497*^9, 3.683214829592606*^9}, {3.683214871668705*^9,
3.683214951721538*^9}, {3.683214985257185*^9, 3.683215138450399*^9}, {
3.683215171841063*^9, 3.683215207996929*^9}, {3.683543889619812*^9,
3.6835438906354933`*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"f", "[", "x", "]"}], ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "0", ",", " ", "0.5"}], "}"}]}], "]"}]], "Input",
CellChangeTimes->{{3.6832143709726954`*^9, 3.683214378512084*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwd1Xk81dkbB3DLKKGShrqYRGhaLCNKio+GhEKWLCWRJNHQpqEyqTRDF1m6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"]]}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0.875},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None},
PlotRange->{{0, 0.5}, {0.87758256678247, 1.}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.683214378844803*^9, {3.6832144156551037`*^9, 3.683214426740994*^9}, {
3.683214466652931*^9, 3.6832144763934402`*^9}, {3.6832145358370123`*^9,
3.683214547668614*^9}, 3.683214607004393*^9, 3.6832146654241533`*^9, {
3.6832146962444983`*^9, 3.683214700625085*^9}, {3.6832147669982233`*^9,
3.6832147949565573`*^9}, 3.6832148308864117`*^9, 3.683214889194956*^9, {
3.683214932363161*^9, 3.68321495395757*^9}, {3.683214989532874*^9,
3.6832151396578608`*^9}, {3.683215179761444*^9, 3.6832152091197777`*^9},
3.683543892287492*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Limit", "[",
RowBox[{
RowBox[{"f", "[", "x", "]"}], ",", " ",
RowBox[{"x", " ", "\[Rule]", " ", "0"}]}], "]"}]], "Input",
CellChangeTimes->{{3.6832148195824003`*^9, 3.683214824164549*^9}}],
Cell[BoxData["1"], "Output",
CellChangeTimes->{{3.683214824461228*^9, 3.683214832128644*^9},
3.6832148904677477`*^9, {3.683214934813483*^9, 3.683214956386396*^9}, {
3.683215017596958*^9, 3.6832151406106377`*^9}, {3.683215185235607*^9,
3.683215200421543*^9}, 3.6835438938241043`*^9}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"data", " ", "=", "\[IndentingNewLine]",
RowBox[{"Table", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Table", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"1", "/",
RowBox[{"2", "^", "i"}]}], ",", " ",
RowBox[{"N", "[",
RowBox[{"f", "[",
RowBox[{"1", "/",
RowBox[{"2", "^", " ", "i"}]}], "]"}], "]"}]}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"i", ",", " ", "1", ",", " ", "n"}], "}"}]}],
"\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"n", ",", " ", "1", ",", " ", "10"}], "}"}]}],
"\[IndentingNewLine]", "]"}]}], ";"}]], "Input",
CellChangeTimes->{{3.683213281504025*^9, 3.68321336409263*^9}, {
3.6832134308264723`*^9, 3.6832135030974703`*^9}, {3.68321392840974*^9,
3.683213928656291*^9}, 3.683214558388567*^9, {3.6832148055377913`*^9,
3.683214807223092*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"TableForm", "[", "data", "]"}]], "Input",
CellChangeTimes->{{3.683544267071076*^9, 3.683544274855958*^9}}],
Cell[BoxData[
InterpretationBox[GridBox[{
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", \
"\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", \
"\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", \
"\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", \
"\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", \
"\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "64"]},
{"0.9998779321710066`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "64"]},
{"0.9998779321710066`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "128"]},
{"0.9999694825770951`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]},
"RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "64"]},
{"0.9998779321710066`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "128"]},
{"0.9999694825770951`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "256"]},
{"0.99999237061517`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], "\<\"\"\>", "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "64"]},
{"0.9998779321710066`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "128"]},
{"0.9999694825770951`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "256"]},
{"0.99999237061517`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "512"]},
{"0.9999980926519735`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], "\<\"\"\>"},
{GridBox[{
{
FractionBox["1", "2"]},
{"0.8775825618903728`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "4"]},
{"0.9689124217106447`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "8"]},
{"0.992197667229329`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "16"]},
{"0.9980475107000991`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "32"]},
{"0.9995117584851364`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "64"]},
{"0.9998779321710066`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "128"]},
{"0.9999694825770951`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "256"]},
{"0.99999237061517`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "512"]},
{"0.9999980926519735`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}], GridBox[{
{
FractionBox["1", "1024"]},
{"0.9999995231628797`"}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.1]},
Offset[0.2]}, "RowsIndexed" -> {}}]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[2.0999999999999996`]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
TableForm[{{{
Rational[1, 2], 0.8775825618903728}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}, {
Rational[1, 64], 0.9998779321710066}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}, {
Rational[1, 64], 0.9998779321710066}, {
Rational[1, 128], 0.9999694825770951}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}, {
Rational[1, 64], 0.9998779321710066}, {
Rational[1, 128], 0.9999694825770951}, {
Rational[1, 256], 0.99999237061517}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}, {
Rational[1, 64], 0.9998779321710066}, {
Rational[1, 128], 0.9999694825770951}, {
Rational[1, 256], 0.99999237061517}, {
Rational[1, 512], 0.9999980926519735}}, {{
Rational[1, 2], 0.8775825618903728}, {
Rational[1, 4], 0.9689124217106447}, {
Rational[1, 8], 0.992197667229329}, {
Rational[1, 16], 0.9980475107000991}, {
Rational[1, 32], 0.9995117584851364}, {
Rational[1, 64], 0.9998779321710066}, {
Rational[1, 128], 0.9999694825770951}, {
Rational[1, 256], 0.99999237061517}, {
Rational[1, 512], 0.9999980926519735}, {
Rational[1, 1024], 0.9999995231628797}}}]]], "Output",
CellChangeTimes->{3.6835442757304983`*^9}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"int", "[",
RowBox[{"i_", ",", " ", "h_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"InterpolatingPolynomial", "[",
RowBox[{
RowBox[{"data", "[",
RowBox[{"[", "i", "]"}], "]"}], ",", " ", "h"}], "]"}], " ", "//", " ",
"N"}]}]], "Input",
CellChangeTimes->{{3.683213376089913*^9, 3.683213414838382*^9}, {
3.683213480413106*^9, 3.683213487134054*^9}, {3.683213522852931*^9,
3.683213523379961*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"Table", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"int", "[",
RowBox[{"i", ",", " ", "x"}], "]"}], " ", "//", " ", "Simplify"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"i", ",", " ", "1", ",", " ", "4"}], "}"}]}],
"\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]",
RowBox[{"TableForm", "[", "%", "]"}]}], "Input",
CellChangeTimes->{{3.683543908095418*^9, 3.683543958939102*^9}}],
Cell[BoxData[
TagBox[
TagBox[GridBox[{
{"0.8775825618903728`"},
{
RowBox[{"1.0602422815309167`", "\[VeryThinSpace]", "-",
RowBox[{"0.3653194392810879`", " ", "x"}]}]},
{
RowBox[{"1.0005631231537122`", "\[VeryThinSpace]", "-",
RowBox[{"0.007244489017860428`", " ", "x"}], "-",
RowBox[{"0.47743326701763666`", " ",
SuperscriptBox["x", "2"]}]}]},
{
RowBox[{"0.9999601267629796`", "\[VeryThinSpace]", "+",
RowBox[{"0.0011974604523942722`", " ", "x"}], "-",
RowBox[{"0.5112010648986556`", " ",
SuperscriptBox["x", "2"]}], "+",
RowBox[{"0.038591769006878884`", " ",
SuperscriptBox["x", "3"]}]}]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
"RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}],
Column],
Function[BoxForm`e$,
TableForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{{3.683543943011242*^9, 3.683543959266983*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"points", " ", "=", " ",
RowBox[{"Table", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{"i", ",", " ",
RowBox[{"Re", "[",
RowBox[{"int", "[",
RowBox[{"i", ",", " ", "0"}], "]"}], "]"}]}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"i", ",", " ", "1", ",", " ", "10"}], "}"}]}],
"\[IndentingNewLine]", "]"}]}]], "Input",
CellChangeTimes->{{3.683213517555332*^9, 3.683213551888112*^9}, {
3.683213614699768*^9, 3.683213615827732*^9}, {3.683213936872109*^9,
3.683213937958345*^9}, {3.683214569294993*^9, 3.683214571248109*^9}}],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"1", ",", "0.8775825618903728`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"2", ",", "1.0602422815309167`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"3", ",", "1.0005631231537122`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"4", ",", "0.9999601267629796`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"5", ",", "0.9999999592110085`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"6", ",", "1.000000000654599`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"7", ",", "1.0000000000000913`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"8", ",", "0.9999999999999997`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"9", ",", "0.9999999999999999`"}], "}"}], ",",
RowBox[{"{",
RowBox[{"10", ",", "1.`"}], "}"}]}], "}"}]], "Output",
CellChangeTimes->{
3.683213552145316*^9, 3.683213616439742*^9, {3.683213877283555*^9,
3.6832139382133007`*^9}, 3.683214042729588*^9, 3.683214088132094*^9,
3.683214151070178*^9, 3.683214438584077*^9, 3.6832144811945*^9, {
3.6832145634022837`*^9, 3.6832145716045313`*^9}, 3.683214812132782*^9, {
3.683214937960658*^9, 3.683214958488968*^9}, {3.683215019907034*^9,
3.68321514283753*^9}, {3.683215202793262*^9, 3.68321522241322*^9},
3.6835438966106*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"ListPlot", "[", "points", "]"}]], "Input",
CellChangeTimes->{{3.683213601480364*^9, 3.6832136201453857`*^9}}],
Cell[BoxData[
GraphicsBox[{{}, {{},
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
AbsoluteThickness[1.6],
PointBox[{{1., 0.8775825618903728}, {2., 1.0602422815309167`}, {3.,
1.0005631231537122`}, {4., 0.9999601267629796}, {5.,
0.9999999592110085}, {6., 1.000000000654599}, {7.,
1.0000000000000913`}, {8., 0.9999999999999997}, {9.,
0.9999999999999999}, {10., 1.}}]}, {}}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0.9989350328987343},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
Method->{},
PlotRange->{{0, 10.}, {0.9990556321768808, 1.0014676177398112`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.683213620524157*^9, 3.683213880453622*^9, {3.683213912494602*^9,
3.683213939084776*^9}, 3.683214093656438*^9, 3.683214450139113*^9,
3.683214483340865*^9, 3.683214575987134*^9, 3.68321481411589*^9, {
3.6832149395760937`*^9, 3.6832149597511797`*^9}, {3.683215023172522*^9,
3.683215143953586*^9}, 3.683215223293007*^9, 3.6835438974359417`*^9}]
}, Open ]]
},
WindowSize->{958, 1179},
WindowMargins->{{0, Automatic}, {Automatic, 19}},
FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 949, 15, 32, "Input"],
Cell[CellGroupData[{
Cell[1532, 39, 253, 6, 32, "Input"],
Cell[1788, 47, 4634, 87, 233, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[6459, 139, 223, 5, 32, "Input"],
Cell[6685, 146, 294, 4, 32, "Output"]
}, Open ]],
Cell[6994, 153, 1033, 25, 187, "Input"],
Cell[CellGroupData[{
Cell[8052, 182, 131, 2, 32, "Input"],
Cell[8186, 186, 31679, 861, 446, "Output"]
}, Open ]],
Cell[39880, 1050, 465, 12, 32, "Input"],
Cell[CellGroupData[{
Cell[40370, 1066, 488, 12, 121, "Input"],
Cell[40861, 1080, 1265, 33, 100, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[42163, 1118, 638, 15, 99, "Input"],
Cell[42804, 1135, 1282, 30, 55, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[44123, 1170, 134, 2, 32, "Input"],
Cell[44260, 1174, 1501, 34, 232, "Output"]
}, Open ]]
}
]
*)
(* End of internal cache information *)
Danny van Dyk