{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["Ellipse","Sheet2"],"not_rendered":{"charts":1,"images":2,"defined_names":19,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Ellipse","index":0,"n_rows":34,"n_cols":16,"rows_kept":34,"merged":[[27,2,27,3]]}
[null,"Contours of the Area Function"]
[null,"            for an Ellipse"]
[]
[null,"This DIGMath module lets you investigate "]
[null,null,"    the contour diagrams"]
[null,"           of the area function A =p a b"]
[null,"     for an ellipse with semiaxes a and b."]
[]
[]
[]
["   Three contours shown correspond to A = 10,  A = 30, and  A = 50."]
[]
["Select another value ( 0 to 50) for A =",{"$nulls":3},{"$f":"G13","v":39},null,39]
[{"$nulls":9},"        Trace along the contours at  a0  =",{"$nulls":3},{"$f":"L15/10","v":3.1}]
[{"$nulls":11},31,{"$f":"a+L15*(b-a)/100","v":-1.52}]
[null,"The interval used is from a = 0  to  a = 10."]
[]
[{"$nulls":9},"        At the tracing point  a0 =",null,null,{"$f":"x0","v":3.1}]
["Click each item below for suggestions and investigations"]
[null,"   Item 1",{"$nulls":7},"   the value of y on the contour with A = 10 is",{"$nulls":5},{"$f":"Sheet2!B11","v":{"v":1.026806084463841,"d":"1.03"}}]
[null,"   Item 2",{"$nulls":7},"   the value of y on the contour with A = 30 is",{"$nulls":5},{"$f":"Sheet2!B24","v":{"v":3.0804182533915228,"d":"3.08"}}]
[null,"   Item 3",{"$nulls":7},"   the value of y on the contour with A = 50 is",{"$nulls":5},{"$f":"Sheet2!B34","v":{"v":5.134030422319205,"d":"5.13"}}]
[null,"   Item 4",{"$nulls":7},{"$f":"\"   the value of y on the contour with A = \"&TEXT(D,\"#\")&\" is\"","v":"   the value of y on the contour with A = 39 is"},{"$nulls":5},{"$f":"Sheet2!B44","v":{"v":4.004543729408979,"d":"4.00"}}]
[]
[]
[]
["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."]

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["a =",-4]
["b =",4]
[]
[]
[]
["A = 10"]
[0.1,{"$f":"10/A7/PI()","v":31.830988618379067}]
[5,{"$f":"10/A8/PI()","v":0.6366197723675814}]
[10,0.3183098861837907]
[]
[{"$f":"x0","v":3.1},1.026806084463841]
[{"$f":"x0","v":3.1},1.026806084463841]
[]
[{"$f":"x0","v":3.1},1.026806084463841]
[]
["A =30"]
[0.1,{"$f":"30/A17/PI()","v":{"v":95.4929658551372,"d":"95.49"}}]
[5,{"$f":"30/A18/PI()","v":{"v":1.909859317102744,"d":"1.91"}}]
[10,{"v":0.954929658551372,"d":"0.95"}]
[]
[{"$f":"x0","v":3.1},{"v":3.0804182533915228,"d":"3.08"}]
[{"$f":"x0+0.2","v":3.3000000000000003},{"v":2.8937262380344606,"d":"2.89"}]
[]
[{"$f":"x0","v":3.1},{"v":3.0804182533915228,"d":"3.08"}]
[]
["A = 50"]
[0.1,{"$f":"50/A27/PI()","v":{"v":159.15494309189535,"d":"159.15"}}]
[5,{"$f":"50/A28/PI()","v":{"v":3.183098861837907,"d":"3.18"}}]
[10,{"v":1.5915494309189535,"d":"1.59"}]
[]
[{"$f":"x0","v":3.1},{"v":5.134030422319205,"d":"5.13"}]
[{"$f":"A31","v":3.1},{"v":5.134030422319205,"d":"5.13"}]
[]
[{"$f":"x0","v":3.1},{"v":5.134030422319205,"d":"5.13"}]
[]
[{"$f":"\"A =\"&TEXT(D,\"#.#\")","v":"A =39."}]
[0.1,{"$f":"D/A37/PI()","v":{"v":124.14085561167836,"d":"124.14"}}]
[5,{"$f":"D/A38/PI()","v":{"v":2.482817112233567,"d":"2.48"}}]
[10,{"$f":"D/A39/PI()","v":{"v":1.2414085561167836,"d":"1.24"}}]
[]
[{"$f":"x0","v":3.1},{"$f":"D/A41/PI()","v":{"v":4.004543729408979,"d":"4.00"}}]
[{"$f":"A41","v":3.1},{"$f":"D/A42/PI()","v":{"v":4.004543729408979,"d":"4.00"}}]
[]
[{"$f":"x0","v":3.1},{"$f":"D/A44/PI()","v":{"v":4.004543729408979,"d":"4.00"}}]