(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 131422, 3116] NotebookOptionsPosition[ 97568, 2516] NotebookOutlinePosition[ 105983, 2660] CellTagsIndexPosition[ 105903, 2655] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", "FirstSlide", CellTags-> "SlideShowHeader",ExpressionUUID->"edc31458-cad1-4ef6-b61e-533684f45001"], Cell["Introdu\[CCedilla]\[ATilde]o \[AGrave] F\[IAcute]sica Computacional I \ (2023.2)", "Title", CellChangeTimes->{{3.837668952851544*^9, 3.837668954905465*^9}, { 3.837668987855983*^9, 3.8376690056199923`*^9}, {3.8701894932049365`*^9, 3.8701894933780613`*^9}, {3.9007466866550817`*^9, 3.9007466867648163`*^9}},ExpressionUUID->"5ea2fc48-13f7-4e7a-86a5-\ 59c6b1d81737"], Cell["Aula 1: introdu\[CCedilla]\[ATilde]o ao Mathematica", "Subtitle", CellChangeTimes->{{3.837669021056449*^9, 3.837669037367819*^9}, { 3.83767901964561*^9, 3.837679047672802*^9}},ExpressionUUID->"858ce7a3-2cc8-4116-aa6b-\ 56b9c958f148"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"7a12bfa1-4c9e-42de-b583-8dd27639b024"], Cell[CellGroupData[{ Cell["O ambiente do notebook", "Section", CellChangeTimes->{{3.837669151671595*^9, 3.837669155101227*^9}, { 3.83767907390877*^9, 3.8376790785654507`*^9}},ExpressionUUID->"8bad51ff-a33a-4628-aa52-\ cd21e7dacc17"], Cell[TextData[{ "Um documento do Mathematica \[EAcute] um \[OpenCurlyDoubleQuote]bloco de \ notas\[CloseCurlyDoubleQuote] (", StyleBox["notebook", FontSlant->"Italic"], "). Para criar um notebook em branco, abra o Mathematica e clique em \ \[OpenCurlyDoubleQuote]New Document\[CloseCurlyDoubleQuote]." }], "Item", CellChangeTimes->{ 3.83766917168499*^9, {3.8376794089923286`*^9, 3.837679417643935*^9}, { 3.837679582011804*^9, 3.8376796121379557`*^9}, {3.837679705333893*^9, 3.837679714150722*^9}, {3.8376960228772984`*^9, 3.8376960309643583`*^9}, { 3.837770219459732*^9, 3.837770220604374*^9}},ExpressionUUID->"0cfbf870-2b92-446e-97e7-\ f3509511092c"], Cell["\<\ Ao cri\[AAcute]-lo, surge um cursor horizontal piscando ao lado de um sinal \ de +. Clicando no sinal, pode-se mudar o tipo de entrada, para, por exemplo, \ incluir coment\[AAcute]rios. O padr\[ATilde]o \[EAcute] inserir instru\ \[CCedilla]\[OTilde]es na linguagem Wolfram, cuja sintaxe ser\[AAcute] \ discutida nesta disciplina.\ \>", "Item", CellChangeTimes->{ 3.83766917168499*^9, {3.8376794089923286`*^9, 3.837679417643935*^9}, { 3.837679582011804*^9, 3.8376796121379557`*^9}, {3.837679705333893*^9, 3.837679791811368*^9}, {3.837695342899251*^9, 3.83769539056539*^9}, { 3.837695869088365*^9, 3.837695917687399*^9}, {3.837695955577986*^9, 3.837695956241584*^9}, {3.837697155060074*^9, 3.837697155060672*^9}, { 3.8376972804903307`*^9, 3.837697307557828*^9}, 3.83769746307154*^9, { 3.837770232630869*^9, 3.8377702341603107`*^9}, {3.8377702793302383`*^9, 3.837770306981689*^9}, {3.838130936731494*^9, 3.8381309372150383`*^9}},ExpressionUUID->"deadb379-1fae-4908-8da3-\ b8598f62bb87"], Cell["\<\ H\[AAcute] outras formas de entrada poss\[IAcute]veis, incluindo um formato \ livre que pode ser \[UAcute]til para descobrir as \ instru\[CCedilla]\[OTilde]es na linguagem Wolfram correspondentes a um certo \ c\[AAcute]lculo. No entanto, aqui n\[ATilde]o vamos explorar essas \ possibilidades.\ \>", "Item", CellChangeTimes->{ 3.83766917168499*^9, {3.8376794089923286`*^9, 3.837679417643935*^9}, { 3.837679582011804*^9, 3.8376796121379557`*^9}, {3.837679705333893*^9, 3.837679791811368*^9}, {3.837695342899251*^9, 3.83769539056539*^9}, { 3.837695869088365*^9, 3.837695917687399*^9}, {3.837695955577986*^9, 3.837695956241584*^9}, {3.837697156221998*^9, 3.837697271056157*^9}, { 3.837697406333715*^9, 3.837697406490138*^9}, {3.837697476206975*^9, 3.8376975075389347`*^9}, {3.838460531432835*^9, 3.83846053643884*^9}},ExpressionUUID->"5bf89d34-6419-4624-93db-\ 8c84e7cfd781"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellChangeTimes->{3.837853046581901*^9}, CellTags-> "SlideShowHeader",ExpressionUUID->"f22975e2-f7f3-4fe3-9669-049b75f3f219"], Cell[CellGroupData[{ Cell["Primeiro contato", "Section", CellChangeTimes->{{3.837669229025901*^9, 3.837669231364442*^9}, { 3.837849235271874*^9, 3.837849243829344*^9}},ExpressionUUID->"7fae2f5e-6766-4d41-a016-\ 2fb216bd8a4a"], Cell[CellGroupData[{ Cell[TextData[{ "No primeiro espa\[CCedilla]o dispon\[IAcute]vel, vamos digitar uma opera\ \[CCedilla]\[ATilde]o simples, como ", StyleBox["4+5", FontFamily->"Source Code Pro"], ". Para concluir a opera\[CCedilla]\[ATilde]o, pressione a tecla ", StyleBox["ENTER", FontFamily->"Courier"], " enquanto segura a tecla ", StyleBox["SHIFT", FontFamily->"Courier"], "." }], "Item", CellChangeTimes->{{3.837606867408963*^9, 3.837606914186123*^9}, { 3.8376085727002363`*^9, 3.837608695832625*^9}, {3.837608879830607*^9, 3.837608893634004*^9}, {3.837609105272407*^9, 3.837609120356205*^9}, { 3.837609218040797*^9, 3.8376092477301283`*^9}, {3.8378492560022306`*^9, 3.8378492938018847`*^9}, {3.837850807551218*^9, 3.837850841649411*^9}, { 3.837851492094214*^9, 3.837851506049065*^9}, 3.837852877903096*^9, 3.83785434686698*^9, {3.837854377710063*^9, 3.837854405861826*^9}, { 3.838191955431794*^9, 3.838192003480262*^9}},ExpressionUUID->"e152f919-3088-4872-bc46-\ 870c52ed6efd"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"4", "+", "5", " "}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.837854323376739*^9, 3.8378543468708344`*^9}, { 3.837854377713546*^9, 3.837854405865121*^9}, 3.8378545034851313`*^9, { 3.838192022160676*^9, 3.8381920226178427`*^9}, {3.838372650463155*^9, 3.838372651192358*^9}, {3.83837289129184*^9, 3.8383728924234247`*^9}, 3.8383729358317327`*^9, 3.838460561470673*^9}, CellLabel->"",ExpressionUUID->"9766dc01-3bcd-4995-85ea-75c71d612946"], Cell["\<\ Note que o Mathematica gera automaticamente os c\[OAcute]digos \ \[OpenCurlyDoubleQuote]In[1]:=\[CloseCurlyDoubleQuote] e \ \[OpenCurlyDoubleQuote]Out[1]=\[CloseCurlyDoubleQuote]. O n\[UAcute]mero \ entre colchetes ordena as entradas executadas desde o in\[IAcute]cio da sess\ \[ATilde]o do Mathematica.\ \>", "Item", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.8378512457643013`*^9, 3.837851298931682*^9}, { 3.837852913417255*^9, 3.8378529160712643`*^9}, {3.837854244141877*^9, 3.837854249170315*^9}, 3.8378543468753967`*^9, 3.837854503489901*^9, { 3.8378547185911827`*^9, 3.837854730448209*^9}, {3.837855999292656*^9, 3.837856037170179*^9}, {3.838192079980998*^9, 3.838192083614266*^9}},ExpressionUUID->"dbab9f92-9ce0-4c68-aa67-\ 159eb3f52918"] }, Closed]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"2596aa0f-0af0-4f5b-84aa-994c9b8f9b48"], Cell[CellGroupData[{ Cell[TextData[{ "Se quiser efetuar alguma opera\[CCedilla]\[ATilde]o com o resultado do \ \[UAcute]ltimo c\[AAcute]lculo, voc\[EHat] pode utilizar o s\[IAcute]mbolo ", StyleBox["%", FontFamily->"Source Code Pro"], ". Por exemplo, vamos calcular o fatorial do resultado anterior:" }], "Item", CellChangeTimes->{{3.8376096288909883`*^9, 3.8376096655092707`*^9}, { 3.837609745556622*^9, 3.837609853665905*^9}, {3.837610136573264*^9, 3.837610227571591*^9}, {3.83761034599016*^9, 3.8376103667229013`*^9}, { 3.837610499675313*^9, 3.837610559310751*^9}, {3.8376127420450687`*^9, 3.837612765467533*^9}, {3.837669383787174*^9, 3.837669383790709*^9}, { 3.838130376400509*^9, 3.838130419847247*^9}, {3.838130455082556*^9, 3.838130462653811*^9}, {3.838130535701674*^9, 3.8381305462868967`*^9}, { 3.838192045319386*^9, 3.838192046500239*^9}},ExpressionUUID->"2143093d-42a2-46be-b47b-\ 807e524c33a1"], Cell[BoxData[ RowBox[{ RowBox[{"%", "!"}], " "}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838130451712677*^9, 3.8381304523040857`*^9}, 3.838131428909882*^9, {3.838192027628151*^9, 3.838192027982638*^9}, 3.838372652791972*^9, 3.838372937394822*^9}, CellLabel->"",ExpressionUUID->"2dfa1943-26f5-49d0-993e-d6aeb56a3038"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"15ce6ed6-fd92-4851-b430-ea4a24f175f7"], Cell[CellGroupData[{ Cell[TextData[{ "Se quisermos nos referir ao pen\[UAcute]ltimo resultado (que nesse caso ser\ \[AAcute] novamente igual a ", StyleBox["9", FontFamily->"Source Code Pro"], "), utilizamos ", StyleBox["%%", FontFamily->"Source Code Pro"], ", como no exemplo a seguir: " }], "Item", CellChangeTimes->{{3.8376096288909883`*^9, 3.8376096655092707`*^9}, { 3.837609745556622*^9, 3.837609853665905*^9}, {3.837610136573264*^9, 3.837610227571591*^9}, {3.83761034599016*^9, 3.8376103667229013`*^9}, { 3.837610499675313*^9, 3.837610559310751*^9}, {3.8376127420450687`*^9, 3.837612765467533*^9}, 3.8376693919261723`*^9, {3.837669428420661*^9, 3.837669430445928*^9}, {3.8381306595868063`*^9, 3.838130721022955*^9}, { 3.838130752927978*^9, 3.838130753251218*^9}, 3.838131428912705*^9, 3.838131486128083*^9, 3.8381315343107357`*^9, {3.838368176409821*^9, 3.838368176871125*^9}},ExpressionUUID->"cedfa05b-1fc2-4c3a-b170-\ 99b066ab1f8d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%%", "+", "3", " "}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838130757816559*^9, 3.838130779737713*^9}, 3.838131486128921*^9, 3.8381315343121767`*^9, 3.838133985321661*^9, { 3.838192060962191*^9, 3.8381920620143642`*^9}, {3.838372657135993*^9, 3.8383726591801*^9}, 3.838372940601076*^9}, CellLabel->"",ExpressionUUID->"454011f5-7ab9-4c29-8154-093254cbf039"], Cell[TextData[{ "Analogamente, o antepen\[UAcute]ltimo resultado pode ser recuperado \ utilizando ", StyleBox["%%%.", FontFamily->"Source Code Pro"], " " }], "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838368164474828*^9, 3.838368238698168*^9}},ExpressionUUID->"484eea7f-3eb6-4338-9752-\ 46b2e9d21f08"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"461b4cd9-bda0-4739-8f0a-71787ab10531"], Cell[CellGroupData[{ Cell[TextData[{ "\[CapitalEAcute] poss\[IAcute]vel tamb\[EAcute]m fazer refer\[EHat]ncia a \ um resultado pela sua ordem indicada entre colchetes, como em \ \[OpenCurlyDoubleQuote]Out[1]\[CloseCurlyDoubleQuote] ou, de forma mais \ geral, \[OpenCurlyDoubleQuote]Out[n]\[CloseCurlyDoubleQuote]. Isso pode ser \ feito com a constru\[CCedilla]\[ATilde]o ", StyleBox["%n", FontFamily->"Source Code Pro"], ", como nos exemplos abaixo:" }], "Item", CellChangeTimes->{{3.838134087536747*^9, 3.838134090019478*^9}, { 3.8381346853642197`*^9, 3.838134688851012*^9}},ExpressionUUID->"4d038e75-2595-4e5f-9d75-\ cd4f7445104d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%1", "+", "3", " "}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838134099954989*^9, 3.8381341054342213`*^9}, 3.83813414863488*^9, {3.8381921052538157`*^9, 3.838192105567341*^9}, 3.8383726624771433`*^9, 3.838372942524637*^9},ExpressionUUID->"b18ef52b-8d55-48da-bf5f-\ 503d54af313b"], Cell[BoxData[ RowBox[{"%2", "/", "224", " "}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838134710832513*^9, 3.838134726123541*^9}, { 3.8381921072115107`*^9, 3.838192107938532*^9}, {3.838372673503673*^9, 3.838372674007371*^9}, 3.838372943514534*^9},ExpressionUUID->"c552ba49-502f-4cb0-8ffb-\ 4f2e06f28d0f"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"39ad342e-5351-473d-adeb-93466dbb31a9"], Cell[CellGroupData[{ Cell["\<\ Se voc\[EHat] est\[AAcute] repetindo os comandos em seu computador, deve ter \ notado que, ap\[OAcute]s cada sa\[IAcute]da, o Mathematica gerou uma barra de \ sugest\[OTilde]es de opera\[CCedilla]\[OTilde]es que podem ser feitas com \ cada resultado, como na figura a seguir. \ \>", "Item", CellChangeTimes->{{3.837613089212138*^9, 3.837613264018572*^9}, { 3.838132893791459*^9, 3.8381331236068783`*^9}, {3.838134275986104*^9, 3.8381342812949047`*^9}, {3.8381347971991673`*^9, 3.838134902198674*^9}, { 3.838134953633506*^9, 3.838134962666169*^9}, 3.838135103214394*^9, { 3.8381402272569723`*^9, 3.838140242683144*^9}, {3.8381403303835373`*^9, 3.838140330407563*^9}, {3.838192129965024*^9, 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No entanto, como o \ mesmo n\[ATilde]o ocorre em outras linguagens de \ programa\[CCedilla]\[ATilde]o, vou continuar usando o s\[IAcute]mbolo de \ multiplica\[CCedilla]\[ATilde]o \[OpenCurlyDoubleQuote]", StyleBox["*", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote]." }], "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 15002.}, CellChangeTimes->{{3.838201862508799*^9, 3.838201911310316*^9}},ExpressionUUID->"7958131e-b031-41c8-9d6a-\ 96d2faacb6c9"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"0b8ee05e-59e6-4752-9418-549092118cc9"], Cell[CellGroupData[{ Cell[TextData[{ "Divis\[ATilde]o: \[OpenCurlyDoubleQuote]", StyleBox["/", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote]" }], "Item", CellChangeTimes->{{3.8381414518782787`*^9, 3.838141469258628*^9}, { 3.838141602785779*^9, 3.838141656258143*^9}},ExpressionUUID->"52b8c6e5-5b95-4bab-8aaf-\ e2793455e6d6"], Cell[BoxData[ RowBox[{"1.0", "/", "2"}]], "Input", CellChangeTimes->{{3.838141920575831*^9, 3.838141932311541*^9}, { 3.838142279619433*^9, 3.838142279726156*^9}},ExpressionUUID->"f3e45c5a-2463-4b8d-894b-\ 8d2fb10c4911"], Cell[BoxData[ RowBox[{"1", "/", "2.0"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10001.}, CellChangeTimes->{{3.838142299758288*^9, 3.838142338239504*^9}},ExpressionUUID->"e7d329e3-59bf-4e43-a820-\ 001d1a2ec4d6"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "/", "2"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10002.}, CellChangeTimes->{{3.838141934320261*^9, 3.838141934677114*^9}, 3.838142241990089*^9, {3.838142283365019*^9, 3.838142284157361*^9}, { 3.838142325418041*^9, 3.8381423547843733`*^9}},ExpressionUUID->"e992ed96-a904-46dd-955a-\ e9d1d1479d31"], Cell["\<\ Note que o resultado da divis\[ATilde]o de n\[UAcute]meros \ \[OpenCurlyDoubleQuote]com v\[IAcute]rgula\[CloseCurlyDoubleQuote] \[EAcute] \ tamb\[EAcute]m um n\[UAcute]mero com v\[IAcute]rgula, enquanto o resultado da \ divis\[ATilde]o entre inteiros \[EAcute] um n\[UAcute]mero racional. Mais \ sobre isso adiante.\ \>", "ItemParagraph", CellMargins:> Dynamic[{{ 0.22000000000000003` FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}], 0.03 FrontEnd`AbsoluteCurrentValue[{WindowSize, 1}]}, { 0.010820636663007685` FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}], 0.011004587486278816` FrontEnd`AbsoluteCurrentValue[{WindowSize, 2}]}}], CellGroupingRules->{"GroupTogetherGrouping", 10002.}, CellChangeTimes->{{3.8381414518782787`*^9, 3.838141469258628*^9}, { 3.838141602785779*^9, 3.838141670153287*^9}, {3.8381419894767733`*^9, 3.8381421133359537`*^9}, 3.838142241991798*^9, {3.8381423254209957`*^9, 3.838142354786976*^9}},ExpressionUUID->"195d5783-5ff9-4ef9-9358-\ 516e2aef19fa"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"eb917580-d963-4648-9fe8-d950ae5a2221"], Cell[CellGroupData[{ Cell[TextData[{ "Potencia\[CCedilla]\[ATilde]o: \[OpenCurlyDoubleQuote]", StyleBox["^", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] " }], "Item", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8381414518782787`*^9, 3.838141469258628*^9}, { 3.838141602785779*^9, 3.838141670153287*^9}, 3.838142241993102*^9, { 3.8381423745524693`*^9, 3.838142380727602*^9}},ExpressionUUID->"5a57b358-3e5e-42e0-a5c8-\ dec00838bf64"], Cell[BoxData[ RowBox[{"2", "^", "3"}]], "Input", CellChangeTimes->{{3.838201930601406*^9, 3.838201932082254*^9}, { 3.83820218066605*^9, 3.838202201491158*^9}}, CellLabel->"",ExpressionUUID->"2c997e88-3dbe-45f9-97ef-747aff5c14ee"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"4b00c780-ad47-4972-80e0-3b0073c6ef6a"], Cell[CellGroupData[{ Cell["Par\[EHat]nteses", "Section", CellChangeTimes->{{3.838201453318037*^9, 3.838201458874305*^9}, { 3.838201937095543*^9, 3.838201939277933*^9}, {3.838201980025552*^9, 3.8382019804978647`*^9}},ExpressionUUID->"d0e1ad9d-4456-49b9-b70e-\ 521be2b52128"], Cell["\<\ Para agrupar opera\[CCedilla]\[OTilde]es de maneira mais clara, e garantir \ que sejam feitas na ordem que voc\[EHat] deseja, utilize par\[EHat]nteses:\ \>", "Text", CellChangeTimes->{{3.838201994280407*^9, 3.838202025520761*^9}, { 3.83820296561345*^9, 3.838202969066165*^9}},ExpressionUUID->"fd620ae9-c9b2-4fd2-b0c8-\ 786f645936cb"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"2", "^", "3"}], ")"}], "^", "4"}]], "Input", CellChangeTimes->{{3.838202032211645*^9, 3.838202039542244*^9}}, CellLabel->"",ExpressionUUID->"d85d1c08-6c9b-42b3-8916-fb45c26fc410"], Cell[BoxData[ RowBox[{"2", "^", RowBox[{"(", RowBox[{"3", "^", "4"}], ")"}]}]], "Input", CellChangeTimes->{{3.838202045339723*^9, 3.838202051250127*^9}},ExpressionUUID->"f3b623bf-4fe5-461f-bcd0-\ ca4574b59325"], Cell[BoxData[ RowBox[{"2", "^", RowBox[{"3", "^", "4"}]}]], "Input", CellChangeTimes->{{3.838202056488647*^9, 3.838202062444296*^9}, { 3.838202114779046*^9, 3.83820211684931*^9}},ExpressionUUID->"daa98b5a-df4a-4740-96d2-\ 044c65964368"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"cf405a71-a5bb-4aac-8f2e-9b663eae43f3"], Cell[CellGroupData[{ Cell["Constantes matem\[AAcute]ticas", "Section", CellChangeTimes->{{3.838203024046138*^9, 3.838203029861177*^9}},ExpressionUUID->"8fa5f292-2992-4050-b486-\ fc42cbebe481"], Cell["\<\ O Mathematica reconhece diversas constantes matem\[AAcute]ticas importantes. \ Exemplos s\[ATilde]o dados a seguir, com uma ou mais formas de \ invoc\[AAcute]-las indicadas entre aspas.\ \>", "Text", CellChangeTimes->{{3.8382104849581347`*^9, 3.838210524062139*^9}, { 3.838210566497718*^9, 3.838210588918832*^9}, {3.838460861453396*^9, 3.838460864029353*^9}},ExpressionUUID->"3d258d4e-1ae7-4756-a40f-\ e25c1f298dc9"], Cell[CellGroupData[{ Cell[TextData[{ "Pi: \[OpenCurlyDoubleQuote]", StyleBox["Pi", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] ou \[OpenCurlyDoubleQuote]", StyleBox["\[Pi]", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] " }], "Item", CellChangeTimes->{{3.838210546496399*^9, 3.838210558173359*^9}, { 3.838210591399419*^9, 3.838210638227528*^9}},ExpressionUUID->"d7683ff9-885c-40e0-9ebf-\ ab6c04a32288"], Cell[TextData[{ "Para produzir a segunda forma acima, h\[AAcute] duas maneiras. A primeira \ delas \[EAcute] ir ao menu \[OpenCurlyDoubleQuote]Palettes\ \[CloseCurlyDoubleQuote], escolher \[OpenCurlyDoubleQuote]Basic Math \ Assistant\[CloseCurlyDoubleQuote] e, na janela que ser\[AAcute] aberta, abrir \ a op\[CCedilla]\[ATilde]o \[OpenCurlyDoubleQuote]Basic Commands\ \[CloseCurlyDoubleQuote] e clicar no s\[IAcute]mbolo ", StyleBox["\[Pi]", FontFamily->"Source Code Pro", FontWeight->"Regular"], ". A segunda forma, muito mais r\[AAcute]pida, \[EAcute] pressionar a tecla \ ESC, digitar \[OpenCurlyDoubleQuote]pi\[CloseCurlyDoubleQuote] (sem aspas) e \ pressionar novamente ESC. Essa combina\[CCedilla]\[ATilde]o de ESC-\ \[OpenCurlyDoubleQuote]nome\[CloseCurlyDoubleQuote]-ESC produz muitos s\ \[IAcute]mbolos \[UAcute]teis." }], "ItemParagraph", CellChangeTimes->{{3.838210654844859*^9, 3.838210759907935*^9}, { 3.838210831019773*^9, 3.838210915293594*^9}, {3.838210980971141*^9, 3.838210981556143*^9}},ExpressionUUID->"e86db94c-402a-481e-b107-\ 3bfdd696ede3"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"4b62b4fe-1260-4954-8402-9c41efa84705"], Cell[CellGroupData[{ Cell[TextData[{ "Pi: \[OpenCurlyDoubleQuote]", StyleBox["Pi", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] ou \[OpenCurlyDoubleQuote]", StyleBox["\[Pi]", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] " }], "Item", CellChangeTimes->{ 3.83821116303176*^9},ExpressionUUID->"2dbbb9f5-35ec-4ba2-8aeb-1bb998ce811d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Pi", "/", "2"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838211167917831*^9, 3.8382111700949383`*^9}, { 3.8382113915280313`*^9, 3.838211400127041*^9}},ExpressionUUID->"b9304b72-ce75-4262-b3a1-\ 2553a75fdeaa"], Cell[TextData[{ "Para produzir um valor num\[EAcute]rico expl\[IAcute]cito de uma constante \ matem\[AAcute]tica, utilize a ", StyleBox["fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca", FontWeight->"Bold"], " ", StyleBox[ButtonBox["N", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/N.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/N.html"], FontFamily->"Source Code Pro"], ":" }], "ItemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.838211232297608*^9, 3.8382112845986767`*^9}, 3.838211400130239*^9, {3.838369807644517*^9, 3.838369808239624*^9}, { 3.8383698389183826`*^9, 3.838369840380989*^9}, {3.900747985459674*^9, 3.900747985462747*^9}},ExpressionUUID->"4ce9deb5-ec54-4e91-abf7-\ 6fdf6247278d"], Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 15001.}, CellChangeTimes->{{3.83821136374968*^9, 3.838211400132111*^9}},ExpressionUUID->"f1c0d994-f1cf-4aae-8322-\ 7169c718cc61"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"4f50c4f2-e232-45d9-9477-8258007a4da4"], Cell[CellGroupData[{ Cell[TextData[{ "O n\[UAcute]mero de Neper: \[OpenCurlyDoubleQuote]", StyleBox["E", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] ou \[OpenCurlyDoubleQuote]", StyleBox["\[ExponentialE]", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote]" }], "Item", CellChangeTimes->{{3.8382110325086823`*^9, 3.838211063898999*^9}, { 3.838211099929459*^9, 3.838211102208156*^9}},ExpressionUUID->"2fd2bbcf-9bc1-4a9b-ad26-\ fce25f48ea17"], Cell[CellGroupData[{ Cell["\<\ Para produzir a segunda forma, utilize o \[OpenCurlyDoubleQuote]Basic Math \ Assistant\[CloseCurlyDoubleQuote] ou digite ESC-\[OpenCurlyDoubleQuote]ee\ \[CloseCurlyDoubleQuote]-ESC. (Note que ap\[OAcute]s voc\[EHat] digitar o \ primeiro \[OpenCurlyDoubleQuote]e\[CloseCurlyDoubleQuote] abre-se um menu com \ os poss\[IAcute]veis s\[IAcute]mbolos e as formas de produzi-los.)\ \>", "ItemParagraph", CellChangeTimes->{{3.838211548807612*^9, 3.838211570643126*^9}, { 3.838211604294541*^9, 3.838211677238173*^9}, 3.838212010903206*^9, { 3.838460996217925*^9, 3.838461001325385*^9}},ExpressionUUID->"1be4a49e-fcb4-469a-b460-\ 0094dac01a62"], Cell[BoxData[ RowBox[{"E", "^", "2"}]], "Input", CellChangeTimes->{{3.8382114995197477`*^9, 3.838211502303885*^9}, { 3.838211539466194*^9, 3.8382115395158987`*^9}},ExpressionUUID->"5be1b485-997e-409f-ad2a-\ a0521ae88b78"], Cell[BoxData[ RowBox[{"N", "[", "\[ExponentialE]", "]"}]], "Input", CellChangeTimes->{{3.838211520751719*^9, 3.838211530314283*^9}}, CellLabel->"",ExpressionUUID->"7ca587f9-e806-4c6d-ad55-59ba0f7180a4"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"a789a3f4-54d8-45c4-8ae4-be00be95f30d"], Cell[CellGroupData[{ Cell[TextData[{ "A unidade imagin\[AAcute]ria: \[OpenCurlyDoubleQuote]", StyleBox["I", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote] ou \[OpenCurlyDoubleQuote]", StyleBox["\[ImaginaryI]", FontFamily->"Source Code Pro"], "\[CloseCurlyDoubleQuote]" }], "Item", CellChangeTimes->{{3.838211809538581*^9, 3.838211826491963*^9}},ExpressionUUID->"610cb0a1-0f17-453e-8193-\ 8f4ca0661430"], Cell[CellGroupData[{ Cell["\<\ Para produzir a segunda forma, utilize o \[OpenCurlyDoubleQuote]Basic Math \ Assistant\[CloseCurlyDoubleQuote] ou digite ESC-\[OpenCurlyDoubleQuote]ii\ \[CloseCurlyDoubleQuote]-ESC.\ \>", "ItemParagraph", CellChangeTimes->{{3.838211981698821*^9, 3.83821200037321*^9}},ExpressionUUID->"c87ffb49-5b6a-41d0-9324-\ 4822eb4dd308"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "I"}], ")"}], "^", "2", " "}]], "Input", CellChangeTimes->{{3.83821192944702*^9, 3.838211939811591*^9}, { 3.838211971862603*^9, 3.838211971946003*^9}, {3.838212033167364*^9, 3.838212048894908*^9}},ExpressionUUID->"05e286e3-7bdf-49d3-ae91-\ bdd9fdb99cec"], Cell[BoxData[ RowBox[{ RowBox[{"N", "[", RowBox[{ RowBox[{"(", RowBox[{"I", "+", "3"}], ")"}], "/", "2"}], "]"}], " "}]], "Input", CellChangeTimes->{{3.83821265443887*^9, 3.838212688489489*^9}},ExpressionUUID->"ecf5d13a-ac5b-4b87-83dc-\ 3381c4da3bad"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"5ca13e62-99b2-47be-8573-2acb0a0b6e62"], Cell[CellGroupData[{ Cell["Algumas fun\[CCedilla]\[OTilde]es matem\[AAcute]ticas", "Section", CellChangeTimes->{{3.838212975597762*^9, 3.838212980109399*^9}},ExpressionUUID->"c6d7de87-834a-40c1-8091-\ f8e6ec82760d"], Cell[TextData[{ "Na verdade, fun\[CCedilla]\[OTilde]es s\[ATilde]o objetos b\[AAcute]sicos \ da linguagem Wolfram, subjacente ao Mathematica. Mesmo quando utilizamos s\ \[IAcute]mbolos aritm\[EAcute]ticos, as entradas s\[ATilde]o convertidas em \ fun\[CCedilla]\[OTilde]es intr\[IAcute]nsecas. Por exemplo, ", StyleBox["2+5", FontFamily->"Source Code Pro"], " equivale a ", StyleBox["Plus[2,5]", FontFamily->"Source Code Pro"], ", forma que faz uso da fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca ", StyleBox[ButtonBox["Plus", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Plus.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Plus.html"], FontFamily->"Source Code Pro"], "." }], "Text", CellChangeTimes->{{3.838213011294039*^9, 3.838213032038109*^9}, { 3.8382131078760347`*^9, 3.8382131176400347`*^9}, {3.838213218583622*^9, 3.838213218921327*^9}, {3.838213270099104*^9, 3.838213360323607*^9}, 3.83821340542654*^9, {3.8382134357552977`*^9, 3.8382134376000023`*^9}, { 3.838461042805071*^9, 3.838461043288547*^9}, {3.900748172975347*^9, 3.900748172977817*^9}},ExpressionUUID->"098d2fc5-1dda-42ae-8aee-\ 6b39ec75a9af"], Cell[TextData[{ StyleBox["Toda fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca do Mathematica \ come\[CCedilla]a com letra mai\[UAcute]scula.", FontWeight->"Bold", FontColor:>Dynamic[ CurrentValue[{StyleHints, "ColorSet", "Display1"}]]], " " }], "Text", CellChangeTimes->{{3.838213475426261*^9, 3.838213505708478*^9}},ExpressionUUID->"24cabc51-1fd9-4384-a4cd-\ a3e63cd73315"], Cell["A seguir, apresentamos algumas das fun\[CCedilla]\[OTilde]es \ \[UAcute]teis em f\[IAcute]sica.", "Text", CellChangeTimes->{{3.838213519963028*^9, 3.8382135305823917`*^9}},ExpressionUUID->"457b561c-0782-4161-a0e6-\ a8f2b1139a19"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"15a7b98c-c30f-490b-ab79-1674ff8482b2"], Cell[CellGroupData[{ Cell[TextData[{ "Raiz quadrada: ", StyleBox[ButtonBox["Sqrt", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Sqrt.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Sqrt.html"], FontFamily->"Source Code Pro"] }], "Item", 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Ap\[OAcute]s a atribui\[CCedilla]\[ATilde]o, podemos \ trabalhar com uma vari\[AAcute]vel em outros c\[AAcute]lculos.\ \>", "Text", CellChangeTimes->{{3.8382287721794653`*^9, 3.838228867012785*^9}, { 3.838229060379628*^9, 3.8382290859281073`*^9}, {3.838298140478827*^9, 3.838298206718047*^9}, {3.838298240715867*^9, 3.838298244619419*^9}, { 3.8384611319047937`*^9, 3.838461175926436*^9}},ExpressionUUID->"3daf50c7-d42d-471f-b001-\ 910fecc66bd1"], Cell[BoxData[ RowBox[{"x", "=", "3"}]], "Input", CellChangeTimes->{{3.838228871187635*^9, 3.8382288726341963`*^9}, { 3.838228997929961*^9, 3.838228997997324*^9}}, CellLabel->"",ExpressionUUID->"3f365a1d-be0b-4928-8d45-f05260b7ae4c"], Cell[BoxData[ RowBox[{"x", "+", "5"}]], "Input", CellChangeTimes->{{3.838228879661446*^9, 3.838228882579192*^9}, { 3.838229000707347*^9, 3.838229000939139*^9}}, CellLabel->"",ExpressionUUID->"f6db6518-1a20-4271-81fa-f823edaac24c"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"Exp", "[", "x", "]"}], "]"}]], "Input", CellChangeTimes->{{3.838229173661783*^9, 3.838229195256459*^9}}, CellLabel->"",ExpressionUUID->"92756c20-91ac-4b82-a730-8c03c513fdba"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"392b3232-c178-4b16-a5a7-4850207cb349"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", "=", RowBox[{"x", "+", "4"}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838228897761757*^9, 3.8382289007746487`*^9}, { 3.8382289834425364`*^9, 3.8382289834969387`*^9}, 3.8382292290244007`*^9}, CellLabel->"",ExpressionUUID->"e59d0732-5f2b-4a30-95b2-ea7ff0ac5bf5"], Cell[TextData[{ "Note que o sinal de igualdade aqui ", StyleBox["n\[ATilde]o", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], " define uma equa\[CCedilla]\[ATilde]o, mas uma ", "atribui\[CCedilla]\[ATilde]o", ". No \[UAcute]ltimo exemplo, redefinimos ", StyleBox["x", FontFamily->"Source Code Pro"], " como tendo seu valor anterior acrescido de ", StyleBox["4", FontFamily->"Source Code Pro"], ", da\[IAcute] o resultado igual a ", StyleBox["7", FontFamily->"Source Code Pro"], ". Esse tipo de constru\[CCedilla]\[ATilde]o \[EAcute] comum a virtualmente \ todas as linguagens de programa\[CCedilla]\[ATilde]o." }], "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8382289026767673`*^9, 3.838229019867982*^9}, 3.838229229028056*^9, {3.838295135932227*^9, 3.838295162334395*^9}, { 3.838298267895919*^9, 3.838298286762211*^9}},ExpressionUUID->"fc9d189f-48d7-435c-a7b3-\ 143cae9735a5"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"abbd2574-f850-4683-b051-bac662a5edd2"], Cell["\<\ Para evitar que uma atribui\[CCedilla]\[ATilde]o ou qualquer \ instru\[CCedilla]\[ATilde]o do Mathematica imprima um resultado, voc\[EHat] \ pode finaliz\[AAcute]-la com ponto-e-v\[IAcute]rgula:\ \>", "Text", CellChangeTimes->{{3.838298810024922*^9, 3.8382988600190287`*^9}},ExpressionUUID->"c6ee2f24-865c-4b72-a4f5-\ 11462cc58f87"], Cell[BoxData[ RowBox[{ RowBox[{"y", "=", "3"}], ";"}]], "Input", CellChangeTimes->{{3.838298868008306*^9, 3.8382988864456577`*^9}},ExpressionUUID->"ad092a3e-7f99-42be-9985-\ 1850ad7eeeff"], Cell[BoxData[ RowBox[{"y", "+", "5"}]], "Input", CellChangeTimes->{{3.838298890244322*^9, 3.8382988907495537`*^9}},ExpressionUUID->"ebd7bde0-9a43-4896-a7dd-\ b35d2cca7530"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"Exp", "[", "y", "]"}], "]"}]], "Input", CellChangeTimes->{{3.838298898937846*^9, 3.8382989049080276`*^9}},ExpressionUUID->"27a2bac3-22ff-4994-8753-\ d01a74de4cf0"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellChangeTimes->{{3.83829880116678*^9, 3.8382988011668043`*^9}}, CellTags-> "SlideShowHeader",ExpressionUUID->"5fc90193-05f0-4811-ae00-74049d76b8ee"], Cell["\<\ Nomes de vari\[AAcute]veis n\[ATilde]o est\[ATilde]o limitados a uma \ \[UAcute]nica letra, mas \[EAcute] uma boa pr\[AAcute]tica n\[ATilde]o \ iniciar os nomes com letras mai\[UAcute]sculas, para evitar conflitos com fun\ \[CCedilla]\[OTilde]es intr\[IAcute]nsecas do Mathematica.\ \>", "Text", CellChangeTimes->{{3.838298567172155*^9, 3.838298615510467*^9}, { 3.83829900668668*^9, 3.838299040019503*^9}, {3.838299074062395*^9, 3.838299099881124*^9}, {3.8383589601852007`*^9, 3.8383589706113377`*^9}},ExpressionUUID->"ab69ef64-ea71-4bcb-b9ad-\ f9dbc47f605c"], Cell[BoxData[ RowBox[{ RowBox[{"tempo", "=", "10"}], ";"}]], "Input", CellChangeTimes->{{3.8382986187748938`*^9, 3.838298631059012*^9}, { 3.8382989188141403`*^9, 3.838298924381476*^9}, {3.8382989725862827`*^9, 3.8382989727895947`*^9}},ExpressionUUID->"da8709de-b346-4aa3-bf32-\ ea5f5d59c958"], Cell[BoxData[ RowBox[{ RowBox[{"velocidade", " ", "=", " ", "3.6"}], ";"}]], "Input", CellChangeTimes->{{3.83829862725704*^9, 3.838298648473886*^9}, 3.838298927144669*^9, {3.8382989688261433`*^9, 3.838298969032967*^9}},ExpressionUUID->"6e983a99-e388-4a9a-b135-\ 08d3b9f43796"], Cell[BoxData[ RowBox[{"deslocamento", " ", "=", " ", RowBox[{"velocidade", " ", "*", " ", "tempo"}]}]], "Input", CellChangeTimes->{{3.8382989791925993`*^9, 3.838298984951035*^9}},ExpressionUUID->"9eba07be-03d2-4c24-8ebd-\ 5fab6d7782e2"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"cd04b5cc-8876-499c-9093-44de37e386a5"], Cell[TextData[{ "Uma vez atribu\[IAcute]do um valor a uma vari\[AAcute]vel, a \ vari\[AAcute]vel permanece ativa em uma mesma sess\[ATilde]o do Mathematica \ at\[EAcute] que esse valor seja \[OpenCurlyDoubleQuote]limpo\ \[CloseCurlyDoubleQuote]. Isso pode ser feito com a fun\[CCedilla]\[ATilde]o \ intr\[IAcute]nseca ", StyleBox[ButtonBox["Clear", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Clear.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Clear.html"], FontFamily->"Source Code Pro"], ":" }], "Text", CellChangeTimes->{{3.838298490433902*^9, 3.838298523800653*^9}, { 3.838367771171822*^9, 3.8383678449489117`*^9}, {3.900748527526669*^9, 3.9007485275291367`*^9}},ExpressionUUID->"773a81e3-5cb6-4a10-b20a-\ 753890f064b1"], Cell[BoxData["x"], "Input", CellChangeTimes->{3.838367861414144*^9}, CellLabel->"",ExpressionUUID->"d63ab30d-8d22-4f29-be56-f13ec57ae0ca"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Clear", "[", "x", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8383678645490217`*^9, 3.838367866035214*^9}, 3.838368053775896*^9}, CellLabel->"",ExpressionUUID->"8f51a880-6ae9-4b1b-9f26-5859cae7eaa8"], Cell["\<\ Note que o Mathematica indica pela cor preta as vari\[AAcute]veis com valores \ atribu\[IAcute]dos e pela cor azul vari\[AAcute]veis sem valor \ atribu\[IAcute]do.\ \>", "SubitemParagraph", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838368013847397*^9, 3.838368053779463*^9}, { 3.9007485542113533`*^9, 3.9007485728024673`*^9}},ExpressionUUID->"05a0fcaa-0868-4377-9832-\ 5c78039b3fe6"] }, Closed]], Cell[BoxData["x"], "Input", CellChangeTimes->{3.8383678679921827`*^9}, CellLabel->"",ExpressionUUID->"1e7c7c23-3e70-4731-a64c-d0dd6cf320a4"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"7b07a84a-33c8-4e37-ad79-b1177085a96d"], Cell[CellGroupData[{ Cell["Formas num\[EAcute]ricas", "Section", CellChangeTimes->{{3.838368340999361*^9, 3.838368359338529*^9}, 3.838368410491561*^9},ExpressionUUID->"885a4bcd-2c4e-4fcf-948d-\ 160308623ff0"], Cell[BoxData[ RowBox[{"expr", "=", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"1.4", "*", RowBox[{"10", "^", RowBox[{"-", "25"}]}]}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"6.9", "*", RowBox[{"10", "^", RowBox[{"-", "2"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{"1.1", "*", RowBox[{"10", "^", RowBox[{"-", "22"}]}]}], ")"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.838368580010149*^9, 3.8383686630756617`*^9}, { 3.838369057625572*^9, 3.838369057816195*^9}, {3.838369383360649*^9, 3.838369383619856*^9}},ExpressionUUID->"da8aac4d-0d9f-46f7-b7b9-\ 7483f80a0893"], Cell[TextData[{ "Para expressar o valor de qualquer c\[AAcute]lculo num\[EAcute]rico ou vari\ \[AAcute]vel com um certo n\[UAcute]mero de algarismos significativos, \ utilize a fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca ", StyleBox[ButtonBox["NumberForm", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/NumberForm.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/NumberForm.html"], FontFamily->"Source Code Pro"], ". Eis um exemplo com 2 algarismos significativos:" }], "Text", CellChangeTimes->{{3.8383688016304197`*^9, 3.838368810246502*^9}, { 3.838368935303563*^9, 3.8383690275079203`*^9}, {3.838369083511191*^9, 3.838369083836865*^9}, {3.838370118089713*^9, 3.8383701394640083`*^9}, { 3.838370186152357*^9, 3.838370193553965*^9}, {3.900748642819826*^9, 3.900748642822418*^9}},ExpressionUUID->"79d4d4ed-5b57-4a82-a8d2-\ b3fa9b15e3ff"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NumberForm", "[", RowBox[{"expr", ",", "2"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838368670691217*^9, 3.838368674461916*^9}, { 3.838368711841775*^9, 3.838368713609692*^9}, {3.838369031618092*^9, 3.838369031856607*^9}, {3.838369101597937*^9, 3.838369102782724*^9}, { 3.838369378238806*^9, 3.838369378455267*^9}, 3.83837245005733*^9},ExpressionUUID->"d39567f7-f7ab-49da-b75c-\ a1f5e536036f"], Cell[TextData[{ "Para expressar um n\[UAcute]mero em nota\[CCedilla]\[ATilde]o \ cient\[IAcute]fica, utilize a fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca ", StyleBox["ScientificForm", FontFamily->"Source Code Pro"], ":" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838369195990099*^9, 3.8383691964052773`*^9}, { 3.838369229953401*^9, 3.83836926866403*^9}, 3.8383724500619173`*^9},ExpressionUUID->"1222ea73-315b-42a7-b674-\ 02a3e25d3ed8"], Cell[BoxData[ RowBox[{"ScientificForm", "[", "expr", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838369271446044*^9, 3.838369284808858*^9}, { 3.838369376135483*^9, 3.8383693763389893`*^9}, 3.8383724398363857`*^9, { 3.838372488112174*^9, 3.838372509053232*^9}},ExpressionUUID->"95d32424-8862-4eaa-91a0-\ cd21f893c501"], Cell["\<\ Um segundo argumento para a fun\[CCedilla]\[ATilde]o estabelece a quantidade \ de algarismos significativos:\ \>", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838370205140346*^9, 3.8383702507720327`*^9}, 3.838372439840954*^9, {3.83837248811526*^9, 3.838372509054528*^9}},ExpressionUUID->"180413aa-00cb-4c02-bc33-\ 1b30029c531e"], Cell[BoxData[ RowBox[{"ScientificForm", "[", RowBox[{"expr", ",", "2"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838370243043664*^9, 3.838370243144024*^9}, 3.8383724398460693`*^9, {3.8383724881165113`*^9, 3.838372509055705*^9}},ExpressionUUID->"ccc9efda-9503-40b6-bab1-\ 4f8384c5d337"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"ae20a7b4-d972-425c-b6ac-abcf16b0cfc1"], Cell[CellGroupData[{ Cell["Exerc\[IAcute]cio", "Subsection", CellChangeTimes->{{3.838371639257243*^9, 3.838371640730225*^9}, { 3.8701894399980793`*^9, 3.870189442516323*^9}},ExpressionUUID->"4ea86357-7f9a-472f-b8cd-\ 57cacc0bc35b"], Cell[TextData[{ "Em uma c\[AHat]mara de v\[AAcute]cuo, atingem-se press\[OTilde]es de at\ \[EAcute] 1.00\[Times]", Cell[BoxData[ FormBox[ SuperscriptBox["10", RowBox[{"-", "9"}]], TraditionalForm]],ExpressionUUID-> "f0480050-1f3c-44e8-8c0b-0948289d2a5f"], " Pa. Calcule o n\[UAcute]mero de mol\[EAcute]culas em um volume de 1.50 ", Cell[BoxData[ FormBox[ SuperscriptBox[ StyleBox["m", FontSlant->"Plain"], "3"], TraditionalForm]],ExpressionUUID-> "ff74420f-08f3-4b86-afe4-ef3dded0e4cb"], " a essa press\[ATilde]o, se a temperatura \[EAcute] de 350 K. " }], "Text", CellChangeTimes->{{3.838371659068686*^9, 3.8383717236989202`*^9}, { 3.8383717634989643`*^9, 3.8383719520971203`*^9}},ExpressionUUID->"844aa3df-253f-497e-b068-\ 2e69c6a3d9db"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"40bdd3b4-fae7-462f-b771-fc62d5630c9d"], Cell[CellGroupData[{ Cell[TextData[{ "Valores exatos ", StyleBox["versus", FontSlant->"Italic"], " valores aproximados" }], "Section", CellChangeTimes->{{3.838372569908291*^9, 3.838372576420766*^9}},ExpressionUUID->"9177baf1-b01c-4ea6-a4c5-\ 29d759bdcd32"], Cell[TextData[{ "O Mathematica trata n\[UAcute]meros inteiros e racionais como exatos. A fun\ \[CCedilla]\[ATilde]o intr\[IAcute]nseca ", StyleBox[ButtonBox["Precision", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/Precision.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/Precision.html"], FontFamily->"Source Code Pro"], StyleBox["[x]", FontFamily->"Source Code Pro"], " fornece o n\[UAcute]mero de algarismos significativos no n\[UAcute]mero ", StyleBox["x", FontFamily->"Source Code Pro"], ". Para n\[UAcute]meros exatos, ", StyleBox["Precision", FontFamily->"Source Code Pro"], " retorna infinito como resultado:" }], "Text", CellChangeTimes->{{3.838373087183323*^9, 3.83837310242766*^9}, { 3.838373184295299*^9, 3.8383732938365507`*^9}, {3.900748685527814*^9, 3.900748685530094*^9}},ExpressionUUID->"77c1c356-97db-4ec2-ba68-\ da0083b73d47"], Cell[BoxData[ RowBox[{"Precision", "[", "5", "]"}]], "Input", CellChangeTimes->{{3.83837329601573*^9, 3.838373298497657*^9}},ExpressionUUID->"8357b10b-28c0-4387-ab7b-\ 59d9f5e6a00a"], Cell[BoxData[ RowBox[{"Precision", "[", RowBox[{"345", "/", "678"}], "]"}]], "Input", CellChangeTimes->{{3.838373301436646*^9, 3.838373309094891*^9}},ExpressionUUID->"f68a6874-2cdd-48cb-a8de-\ 764a99603e74"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"b23bd639-6417-4adb-98b4-f6000fac7205"], Cell["\<\ Quando fornecemos em uma entrada apenas valores exatos, o Mathematica tenta \ retornar resultados exatos:\ \>", "Text", CellChangeTimes->{{3.838373488385137*^9, 3.838373527703431*^9}},ExpressionUUID->"b1a8c7a2-b3c1-4808-a213-\ c018829323d6"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"123", "/", "456"}], " ", "+", " ", RowBox[{"456", "/", "789"}], "+", RowBox[{"2", "*", RowBox[{"Sqrt", "[", "5", "]"}]}]}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8383735302708817`*^9, 3.838373589063888*^9}, 3.838461361366395*^9},ExpressionUUID->"46300f87-6b6f-47a7-8f2e-\ a467a434bd2a"], Cell["Note que o Mathematica considera a raiz de 5 como exata:", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838373614892241*^9, 3.838373647415639*^9}, 3.838461361383622*^9},ExpressionUUID->"6b628814-c795-4d20-b9d7-\ a72a496289f3"], Cell[BoxData[ RowBox[{"Precision", "[", RowBox[{"Sqrt", "[", "5", "]"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838373649846562*^9, 3.838373654503304*^9}, 3.838461361386304*^9},ExpressionUUID->"f71a9705-2af4-4071-9b57-\ 1e10c78a78aa"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"63e83ccb-3a23-485b-a841-32eb71c378b9"], Cell["Isso vale para as demais fun\[CCedilla]\[OTilde]es \ intr\[IAcute]nsecas:", "Text", CellChangeTimes->{{3.838375362931817*^9, 3.8383753995945263`*^9}},ExpressionUUID->"5b0a39e8-f315-4fac-b04b-\ a494f2b285b5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Cos", "[", RowBox[{"Pi", "/", "9"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838375464352613*^9, 3.838375466996612*^9}, 3.8383756323382177`*^9},ExpressionUUID->"fbac4975-1518-4dac-a294-\ 509b01ae0c4d"], Cell["\<\ O Mathematica n\[ATilde]o forneceu um valor num\[EAcute]rico porque \ n\[ATilde]o converte n\[UAcute]meros exatos para valores num\[EAcute]ricos a \ n\[ATilde]o ser que solicitemos explicitamente:\ \>", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8383754827224703`*^9, 3.8383755384091663`*^9}, 3.838375632342237*^9},ExpressionUUID->"f2d4a454-6a2a-40a4-8f37-\ 24faacfa343b"], Cell[BoxData[ RowBox[{"Cos", "[", RowBox[{"N", "[", RowBox[{"Pi", "/", "9"}], "]"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838375550460957*^9, 3.8383755578164473`*^9}, { 3.838375599140201*^9, 3.838375632344261*^9}},ExpressionUUID->"89b3adc9-5190-4a5d-a044-\ cb11f38f8ffb"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"1480536f-c0e1-4f56-818d-497607c8b260"], Cell[CellGroupData[{ Cell[TextData[{ "Precis\[ATilde]o de m\[AAcute]quina ", StyleBox["versus", FontSlant->"Italic"], " precis\[ATilde]o arbitr\[AAcute]ria" }], "Section", CellChangeTimes->{{3.838375832441578*^9, 3.838375850181669*^9}},ExpressionUUID->"662eaa42-ffa2-4cf3-8bbe-\ 85d762b4bbec"], Cell[TextData[{ "O Mathematica pode tratar n\[UAcute]meros reais aproximados tanto como n\ \[UAcute]meros de precis\[ATilde]o arbitr\[AAcute]ria quanto com \ \[OpenCurlyDoubleQuote]", StyleBox["precis\[ATilde]o de m\[AAcute]quina", FontWeight->"Bold"], "\[CloseCurlyDoubleQuote], a qual em geral depende da arquitetura do \ computador utilizado. " }], "Text", CellChangeTimes->{{3.838375908109189*^9, 3.8383760317800493`*^9}, { 3.838376091945767*^9, 3.838376092428872*^9}, {3.838376338496994*^9, 3.838376340139411*^9}, {3.838384045866508*^9, 3.838384046506611*^9}, { 3.838461402244372*^9, 3.838461414383134*^9}},ExpressionUUID->"0b3e95e4-2125-4a18-9521-\ 0709fbc7c884"], Cell[BoxData[ RowBox[{"Precision", "[", "Pi", "]"}]], "Input", CellChangeTimes->{{3.838376107813126*^9, 3.838376111107827*^9}},ExpressionUUID->"fb1adf3e-26f6-49c7-8f5f-\ 31bbd1cd0a7c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precision", "[", RowBox[{"N", "[", "Pi", "]"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8383761141934853`*^9, 3.83837612166887*^9}, 3.8383763304204617`*^9},ExpressionUUID->"222fa7bd-0f4f-430f-9276-\ e3980e314a31"], Cell[TextData[{ "Para saber o valor num\[EAcute]rico de ", StyleBox["MachinePrecision", FontFamily->"Source Code Pro"], ", execute ", StyleBox["$MachinePrecision", FontFamily->"Source Code Pro"], ":" }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838376154691825*^9, 3.838376168462606*^9}, { 3.838376203428879*^9, 3.838376258171473*^9}, 3.838376330424584*^9, { 3.838376376129487*^9, 3.8383763815398493`*^9}},ExpressionUUID->"62979882-1ecd-402c-af50-\ 70fa1ad2b549"], Cell[CellGroupData[{ Cell[BoxData["$MachinePrecision"], "Input", CellChangeTimes->{{3.8383762601372643`*^9, 3.83837626197323*^9}, 3.838376330427017*^9, 3.900749303561474*^9},ExpressionUUID->"484dde14-c3e6-4c73-842d-\ a85b670e2679"], Cell[CellGroupData[{ Cell["\<\ Isso indica o m\[AAcute]xima quantidade de casas decimais guardadas na \ representa\[CCedilla]\[ATilde]o de um n\[UAcute]mero. Por que essa quantidade \ n\[ATilde]o \[EAcute] inteira?\ \>", "Text", CellGroupingRules->{"GroupTogetherGrouping", 10002.}, CellChangeTimes->{{3.900748956764626*^9, 3.9007489737015057`*^9}, { 3.900749064606563*^9, 3.900749151727332*^9}, {3.900749219272356*^9, 3.900749230439411*^9}, {3.90074928603549*^9, 3.900749325591943*^9}},ExpressionUUID->"cba9fa0a-6706-4876-b36e-\ 6b9e43920f90"], Cell[BoxData[ RowBox[{"Log", "[", RowBox[{"2", ",", RowBox[{"10", "^", "$MachinePrecision"}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10002.}, CellChangeTimes->{{3.90074923561052*^9, 3.900749248872102*^9}, { 3.90074928603615*^9, 3.900749325592511*^9}},ExpressionUUID->"ea653c5f-26ce-4fb5-bc01-\ 705c09297225"] }, Open ]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"73a8740d-8c66-4020-9fc7-4975919dbb9f"], Cell["\<\ A menos que especifiquemos de modo contr\[AAcute]rio, o Mathematica considera \ n\[UAcute]meros reais informados com menos do que a precis\[ATilde]o de m\ \[AAcute]quina como tendo essa precis\[ATilde]o:\ \>", "Text", CellChangeTimes->{{3.83837656824693*^9, 3.838376637265525*^9}},ExpressionUUID->"b288de1c-0f26-4a24-a14b-\ 77ec0945ffd4"], Cell[BoxData[ RowBox[{"Precision", "[", "3.14159", "]"}]], "Input", CellChangeTimes->{{3.838376640273182*^9, 3.838376644670477*^9}},ExpressionUUID->"2ef6d621-d1e5-4bb0-8243-\ 11a694f84c8c"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"f0755761-fac5-4ea6-8c49-ce987d092fb3"], Cell["\<\ Se n\[UAcute]meros com precis\[ATilde]o de m\[AAcute]quina aparecem em um c\ \[AAcute]lculo, o resultado tem essa mesma precis\[ATilde]o:\ \>", "Text", CellChangeTimes->{{3.838376669283866*^9, 3.838376694212882*^9}},ExpressionUUID->"0aa57466-a7f9-4572-869f-\ f39004888090"], Cell[BoxData[ RowBox[{"Sqrt", "[", RowBox[{"1.0", "+", "40", "+", RowBox[{"2", "/", "3"}]}], "]"}]], "Input", CellChangeTimes->{{3.838376701991414*^9, 3.8383767100297413`*^9}},ExpressionUUID->"7fba2352-ef34-4fcc-b77f-\ 3314df51f9ca"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Precision", "[", "%", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.83837671281166*^9, 3.838376716772979*^9}, 3.838384560753499*^9},ExpressionUUID->"8dccfaea-5433-4104-814c-\ d50da76fc62c"], Cell[TextData[{ "Note que os resultados do Mathematica, por padr\[ATilde]o, s\[ATilde]o \ impressos apenas com seis algarismos. Para ver os demais d\[IAcute]gitos, \ utilize a fun\[CCedilla]\[ATilde]o intr\[IAcute]nseca ", StyleBox[ButtonBox["InputForm", BaseStyle->"Hyperlink", ButtonData->{ URL["https://reference.wolfram.com/language/ref/InputForm.html"], None}, ButtonNote->"https://reference.wolfram.com/language/ref/InputForm.html"], FontFamily->"Source Code Pro"], ": " }], "Text", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838376762276949*^9, 3.838376861411261*^9}, 3.83838456075879*^9, {3.9007495160894547`*^9, 3.900749516096635*^9}},ExpressionUUID->"f23b2d6b-9164-41b4-96e6-\ b7c63035e417"], Cell[BoxData[ RowBox[{"InputForm", "[", "%%", "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.838376883184285*^9, 3.8383768876922693`*^9}, 3.838384560764072*^9},ExpressionUUID->"13a1e706-3cad-4ce2-9ec2-\ d31aea267fdc"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"9fce1fee-889e-4e17-abec-838ae9739f9a"], Cell[TextData[{ "J\[AAcute] a ", StyleBox["precis\[ATilde]o arbitr\[AAcute]ria", FontWeight->"Bold"], " pode ser obtida com o aux\[IAcute]lio da fun\[CCedilla]\[ATilde]o intr\ \[IAcute]nseca ", StyleBox["N", FontFamily->"Source Code Pro"], ". Por exemplo, vamos expressar ", StyleBox["\[Pi] c", FontFamily->"Source Code Pro", FontWeight->"Regular"], "om 200 algarismos significativos:" }], "Text", CellChangeTimes->{{3.838384092118677*^9, 3.8383841965258904`*^9}, { 3.900750060528117*^9, 3.900750073854713*^9}, {3.9007501040555563`*^9, 3.900750121271124*^9}},ExpressionUUID->"ff29c628-70dd-4c52-9612-\ 51969e849f41"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"Pi", ",", "200"}], "]"}]], "Input", CellChangeTimes->{{3.8383842008050613`*^9, 3.8383842035389423`*^9}}, CellLabel->"",ExpressionUUID->"febaaeac-d57d-45ed-a80f-6e279bfd4f94"], Cell[BoxData[ RowBox[{"Precision", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.8383842208324957`*^9, 3.8383842245314503`*^9}, 3.838384285696594*^9}, CellLabel->"",ExpressionUUID->"b5fb8f18-f852-4c5d-a509-4e36b51840d5"] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags-> "SlideShowHeader",ExpressionUUID->"24b65386-a0ea-4215-add7-061ca33bef3d"], Cell[TextData[{ "Qual \[EAcute] a diferen\[CCedilla]a entre as fun\[CCedilla]\[OTilde]es \ intr\[IAcute]nsecas ", StyleBox["N", FontFamily->"Source Code Pro"], " e ", StyleBox["NumberForm", FontFamily->"Source Code Pro"], "?" }], "Text", CellChangeTimes->{{3.838384295235037*^9, 3.838384328479435*^9}},ExpressionUUID->"52b128f7-14c0-48cc-aa80-\ 73c4facb6623"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NumberForm", "[", RowBox[{"Pi", ",", "200"}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{{3.8383842208324957`*^9, 3.8383842245314503`*^9}, 3.838384285696594*^9, {3.838384331393578*^9, 3.8383843401675243`*^9}, 3.838384632827757*^9}, CellLabel->"",ExpressionUUID->"14b99dda-310b-464f-8c9b-3271b0584bb9"], Cell[TextData[{ "Note que ", StyleBox["NumberForm", FontFamily->"Source Code Pro"], " n\[ATilde]o converte n\[UAcute]meros exatos em n\[UAcute]meros de precis\ \[ATilde]o finita, ao contr\[AAcute]rio do que faz ", StyleBox["N", FontFamily->"Source Code Pro"], ". 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