{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Select Points","Random Points","Sheet2"],"not_rendered":{"charts":3,"images":5,"defined_names":1,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Select Points","index":0,"n_rows":35,"n_cols":10,"rows_kept":35,"merged":[[28,2,28,3]]}
["   Derivative of the Logarithmic Function"]
[{"$nulls":8},{"$f":"C11^H2","v":1}]
[null,"This graphing utility lets you find the formula "]
[null," for the derivative of the natural log function "]
[{"$nulls":3},"y = ln (x)"]
[null,"   using data analysis/curve fitting methods."]
[]
["Enter the x-values for four points on the log curve"]
[null,"Each x-value must be between 0.5 and 5."]
[]
[null,null,{"$f":"D11/100+0.5","v":0.79},29]
[]
[null,null,{"$f":"D13/100+0.5","v":2.08},158,{"$nulls":4},"The graph of the natural logarithm function "]
[{"$nulls":9},"with four points and tangent lines drawn"]
[null,null,{"$f":"D15/100+0.5","v":1.23},73]
[{"$nulls":3},3]
[null,null,{"$f":"D17/100+0.5","v":3.07},257]
[{"$nulls":8},"   "]
[]
[]
["Click each item below for suggestions and investigations"]
["   Item 1"]
["   Item 2"]
["   Item 3"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":7},"The graph of the four slope values "]
["      Click this link:",null,"DIGMath for Calculus",{"$nulls":6},"and the associated power function."]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Random Points","index":1,"n_rows":30,"n_cols":4,"rows_kept":30,"merged":[[23,2,23,3]]}
["   Derivative of the Logarithmic Function"]
[]
[null,"This graphing utility lets you find the formula "]
[null," for the derivative of the natural log function "]
[{"$nulls":3},"y = ln (x)"]
[null,"   using data analysis/curve fitting methods."]
[]
[]
[null,"The program now generates 20 random points "]
[null,null,"on the curve y = ln  x,"]
["calculates the slope of the tangent line at each point,"]
[null,"      and plots those 20 slopes in the chart."]
[]
[null,"It also calculates the power  regression function"]
[null,null,"that fits these 20 points."]
["    The resulting power function equation is also shown."]
[]
[]
[]
[{"$nulls":3},true]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Sheet2","index":2,"n_rows":23,"n_cols":10,"rows_kept":23}
["x","ln x",{"$nulls":4},"random x","log values","ln(x+.0001)","slope"]
[{"$f":"'Select Points'!C11","v":0.79},{"$f":"LN(A2)","v":-0.23572233352106983},{"$f":"C12","v":1.2657426762041624}]
[{"$f":"'Select Points'!C13","v":2.08},{"$f":"LN(A3)","v":0.7323678937132266},{"$f":"C15","v":0.4807576741883146},{"$nulls":3},{"$f":"0.5+4.5*RAND()","v":1.9944039099275517},{"$f":"LN(G3)","v":0.6903452136783338},{"$f":"LN(G3+0.0001)","v":0.6903953527161542},{"$f":"(I3-H3)/0.0001","v":0.5013903782036255}]
[{"$f":"'Select Points'!C15","v":1.23},{"$f":"LN(A4)","v":0.20701416938432612},{"$f":"C18","v":0.8129750827612359},{"$nulls":3},2.496789291215914,0.915005622961676,0.9150456735970394,0.4005063536338671]
[{"$f":"'Select Points'!C17","v":3.07},{"$f":"LN(A5)","v":1.1216775615991057},{"$f":"C21","v":0.325727594043812},{"$nulls":3},3.755000739007685,1.3230884820223863,1.3231151128209977,0.266307986114267]
[{"$nulls":6},3.283574617405666,1.1889326513505318,1.1889631055015568,0.3045415102498339]
[0.5,{"$f":"LN(A7)","v":-0.6931471805599453},{"$nulls":4},3.093999016507048,1.1294644342797986,1.129496754388328,0.32320108529493297]
[5,{"$f":"LN(A8)","v":1.6094379124341003},{"$nulls":4},0.7758151056718716,-0.2538410530755077,-0.25371216469090657,1.288883846011224]
[{"$nulls":6},4.226107810225859,1.4412814300435335,1.44130509219826,0.23662154726489248]
[null,null,"slopes",{"$nulls":3},1.3818139207381228,0.32339707137274715,0.3234694373984772,0.7236602573007511]
[{"$f":"A2","v":0.79},{"$f":"LN(A11)","v":-0.23572233352106983},null,{"$f":"A11","v":0.79},{"$f":"B11","v":-0.23572233352106983},null,3.3691788671274345,1.2146690550683432,1.2146987354503982,0.2968038205497514]
[{"$f":"A11+0.0001","v":0.7901},{"$f":"LN(A12)","v":-0.23559575925344942},{"$f":"(B12-B11)/0.0001","v":1.2657426762041624},{"$f":"A12","v":0.7901},{"$f":"B12+C12*(A12-A11)","v":-0.23546918498582903},null,1.1064116164900561,0.10112200067162337,0.10121237886330912,0.9037819168575267]
[{"$f":"A11+0.8","v":1.59},{"$f":"LN(A13)","v":0.4637340162321402},null,1.59,{"$f":"B12+C12*(A13-A11)","v":0.7769983817098804},null,4.396468509165734,1.4808016071058732,1.4808243523757487,0.22745269875557028]
[{"$f":"A3","v":2.08},0.7323678937132266,null,2.08,{"$f":"B15","v":0.7324159694806455},null,1.2973273861674168,0.2603062914987518,0.2603833700736643,0.7707857491251469]
[{"$f":"A14+0.0001","v":2.0801000000000003},0.7324159694806455,{"$f":"(B15-B14)/0.0001","v":0.4807576741883146},2.0801000000000003,{"$f":"B15+C15*(A15-A14)","v":0.7324640452480644},null,1.313935478152879,0.2730268154723933,0.2731029198142684,0.7610434187504955]
[{"$f":"A14+0.8","v":2.88},null,null,2.88,{"$f":"B15+C15*(A16-A14)","v":1.117022108831297},null,2.4376711671038374,0.8910431438259621,0.8910841657448606,0.41021918898542786]
[{"$f":"A4","v":1.23},0.20701416938432612,null,1.23,{"$f":"B18","v":0.20709546689260225},null,3.1803863432679087,1.1570026810062615,1.1570341232328039,0.31442226542388596]
[{"$f":"A17+0.0001","v":1.2301},0.20709546689260225,{"$f":"(B18-B17)/0.0001","v":0.8129750827612359},1.2301,{"$f":"B18+C18*(A18-A17)","v":0.20717676440087837},null,0.7145876177178584,-0.3360496611138188,-0.3359097300526993,1.399310611194804]
[{"$f":"A17+0.8","v":2.0300000000000002},null,null,2.0300000000000002,{"$f":"B18+C18*(A19-A17)","v":0.8574755331015912},null,1.2488257778053902,0.22220373206673125,0.22228380408176315,0.8007201503190675]
[{"$f":"A5","v":3.07},1.1216775615991057,null,3.07,{"$f":"B21","v":1.12171013435851},null,4.876171655889377,1.5843604152424746,1.5843809229238435,0.2050768136885317]
[{"$f":"A20+0.0001","v":3.0701},1.12171013435851,{"$f":"(B21-B20)/0.0001","v":0.325727594043812},3.0701,{"$f":"B20+C20*(A21-A19)","v":1.1216775615991057},null,4.81646500754889,1.5720402580690194,1.5720610199684106,0.20761899391263938]
[{"$f":"A20+0.8","v":3.87},null,null,3.87,{"$f":"B21+C21*(A22-A20)","v":1.38229220959356},null,2.580266883377422,0.9478928367531937,0.9479315916831238,0.38754929930107096]
[{"$nulls":6},2.71828,0.999999327347282,1.000036114639484,0.36787292202022925]