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Cell[CellGroupData[{ Cell[TextData[{ " ", StyleBox["Dada la tabla ", FontSize->12], StyleBox["b = { (1,1.5), (2,1),(3, 0.73),(4, 0.6), (5,0.3),(6, 0.2),(7, \ 0.1),(8, 0.08)}", FontSize->12, FontWeight->"Bold"], StyleBox["\n a) Dibujar los puntos de la tabla\n b) Calcular una tabla \"c\" \ con los logaritmos neperianos de los puntos de la tabla \"b\"\nc) Realizar un \ ajuste de la tabla \"b\" calculando una aproximaci\[OAcute]n lineal de la \ tabla \"c\" \nd) Dibujar simultaneamente la funci\[OAcute]n de aproximaci\ \[OAcute]n y los puntos de la tabla \"b\".\n\n ", FontSize->12] }], "Section", TextAlignment->Left, TextJustification->1, FontFamily->"Arial", FontSize->14], Cell["\<\ Cuando se intuye que los datos se ajustan bien a una exponencial. Para \ confirmarlo se pueden representar los logaritmos neperianos de los datos y \ ver si se pueden ajustar a una funci\[OAcute]n lineal. Se puede realizar el ajuste lineal y luego deshacer el cambio o bien realizar \ el ajuste utilizando la base exponencial.\ \>", "Text", TextAlignment->Left, TextJustification->1, FontSize->14], Cell["Error cuadr\[AAcute]tico", "Subsection"], Cell["Error del ajuste", "Subsection"], Cell["Ajuste mediante una recta de la tabla inicial", "Subsection"], Cell["\<\ Error cuadr\[AAcute]tico = error del ajuste \ \>", "Subsection", CellChangeTimes->{3.5063429895*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problema 3", "Subtitle", FontSize->16], Cell[CellGroupData[{ Cell[TextData[{ " Dada la siguiente tabla \nd={(1,2), (2,1.5), (3,1.33), (4,1.25),(5, \ 1.2),(6, 1.17),(7,1.14), (8,1.13),(9,1.11),(10, 1.1),(11, 1.09),(12, \ 1.08),(13, 1.07),(14, 1.06),(15, 1.05)}\n a) Estudiar de las siguientes \ funciones a cual de ellas se podr\[IAcute]a ajustar:\n \ty = b.Exp(cx)\n \ y = ", Cell[BoxData[ RowBox[{"1", "/", RowBox[{"(", RowBox[{ RowBox[{"a", " ", "x"}], "+", "b"}], ")"}]}]]], "\n \ty =", StyleBox[" ", FontSize->16], "a/x+b\n b) Realizar el cambio de variable correspondiente para \ linealizar la funci\[OAcute]n y obtener la funci\[OAcute]n de aproximaci\ \[OAcute]n a los puntos de la Tabla \"d\".\n \n " }], "Section", FontFamily->"Arial", FontSize->12], Cell["\<\ Al representar gr\[AAcute]ficamente los puntos se ve que no se ajustan a una \ recta. A continuaci\[OAcute]n se toman logaritmos y se representan los nuevos \ puntos.\ \>", "Text", TextAlignment->Left, TextJustification->1], Cell["Al tomar los inversos tampoco se obtiene una recta.", "Text"], Cell["\<\ Al sustituir x por 1/x s\[IAcute] se obtiene una recta, luego parece que la \ funci\[OAcute]n a la que mejor se ajustar\[IAcute]a es : y= (a/x) + b.\ \>", "Text"], Cell["\<\ A este mismo resultado se puede llegar utilizando como funciones de \ aproximaci\[OAcute]n 1 y 1/x. \ \>", "Text", CellChangeTimes->{3.506343035078125*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problema 4. Ajuste continuo", "Subtitle", FontSize->16], Cell["\<\ Dada la funci\[OAcute]n Cos[x], a) Realizar un ajuste continuo mediante un polinomio de grado dos b) Dibujar simultaneamentre la funcion Cos[x] y el polinomio c)Dibujar la funcion diferencia. d) realizar el mismo proceso mediante un polinomio de grado cuatro \ \>", "Section", FontFamily->"Arial", FontSize->12] }, Open ]] }, Open ]] }, WindowToolbars->"EditBar", WindowSize->{1672, 933}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, Magnification->1.25, FrontEndVersion->"8.0 for Microsoft Windows (32-bit) (November 7, 2010)", StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", CharacterEncoding -> "WindowsANSI"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "Fit"->{ Cell[2338, 94, 208, 6, 47, "Input", CellTags->"Fit"], Cell[2549, 102, 511, 13, 315, "Output", CellTags->"Fit"], Cell[3582, 132, 212, 7, 47, "Input", CellTags->"Fit"], Cell[3797, 141, 204, 5, 47, "Output", CellTags->"Fit"], Cell[9048, 266, 250, 8, 51, "Input", CellTags->"Fit"], Cell[9301, 276, 282, 7, 47, "Output", CellTags->"Fit"]} } *) (*CellTagsIndex CellTagsIndex->{ {"Fit", 19151, 546} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 143, 3, 101, "Title"], Cell[725, 27, 44, 1, 25, "Subtitle"], Cell[CellGroupData[{ Cell[794, 32, 116, 5, 91, "Section"], Cell[913, 39, 557, 18, 85, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[1507, 62, 231, 8, 82, "Section"], Cell[CellGroupData[{ Cell[1763, 74, 191, 6, 47, "Input"], Cell[1957, 82, 344, 7, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2338, 94, 208, 6, 47, "Input", CellTags->"Fit"], Cell[2549, 102, 511, 13, 315, "Output", CellTags->"Fit"] }, Open ]], Cell[3075, 118, 482, 10, 117, "Text"], Cell[CellGroupData[{ Cell[3582, 132, 212, 7, 47, "Input", CellTags->"Fit"], Cell[3797, 141, 204, 5, 47, "Output", CellTags->"Fit"] }, Open ]], Cell[CellGroupData[{ Cell[4038, 151, 198, 6, 47, "Input"], Cell[4239, 159, 2104, 40, 304, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6380, 204, 82, 2, 47, "Input"], Cell[6465, 208, 2257, 42, 304, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8759, 255, 44, 0, 27, "Subsubsection"], Cell[8806, 257, 217, 5, 55, "Text"], Cell[CellGroupData[{ Cell[9048, 266, 250, 8, 51, "Input", CellTags->"Fit"], Cell[9301, 276, 282, 7, 47, "Output", CellTags->"Fit"] }, Open ]], Cell[CellGroupData[{ Cell[9620, 288, 198, 6, 47, "Input"], Cell[9821, 296, 2113, 40, 311, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11971, 341, 82, 2, 47, "Input"], Cell[12056, 345, 2264, 42, 308, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[14381, 394, 65, 1, 25, "Subtitle"], Cell[14449, 397, 756, 10, 202, "Section"] }, Open ]], Cell[CellGroupData[{ Cell[15242, 412, 45, 1, 25, "Subtitle"], Cell[CellGroupData[{ Cell[15312, 417, 677, 18, 205, "Section"], Cell[15992, 437, 410, 9, 61, "Text"], Cell[16405, 448, 46, 0, 31, "Subsection"], Cell[16454, 450, 38, 0, 30, "Subsection"], Cell[16495, 452, 67, 0, 30, "Subsection"], Cell[16565, 454, 112, 4, 53, "Subsection"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[16726, 464, 45, 1, 25, "Subtitle"], Cell[CellGroupData[{ Cell[16796, 469, 756, 19, 250, "Section"], Cell[17555, 490, 235, 6, 34, "Text"], Cell[17793, 498, 67, 0, 34, "Text"], Cell[17863, 500, 173, 3, 34, "Text"], Cell[18039, 505, 166, 5, 55, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[18254, 516, 62, 1, 25, "Subtitle"], Cell[18319, 519, 329, 8, 161, "Section"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)