{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":2,"images":1,"macros":1,"defined_names":12,"comments":1},"read":"whole","date_system":"1900"}

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[null,"      The Osculating Circle"]
[]
[null," This graphing utility lets you investigate "]
[null,"                       the osculating circle "]
[null,null,"whose radius = 1/curvature"]
[null,null,"    at any given point x0"]
[null,"     associated with any desired function"]
[{"$nulls":3},"y = f(x)"]
[null,"   on any interval from x = a  to x = b."]
[]
[]
["   Enter the function in terms of x:   f(x)  = ",{"$nulls":4},"exp(-x)"]
[]
[]
["Now enter the interval for x:  "]
[null,null,"xMin =",-3,{"$nulls":8},"Select a point x0 on the curve =",{"$nulls":3},{"$f":"P18","v":2.3600000000000003}]
[null,null,"xMax =",5]
[{"$nulls":14},67,{"$f":"D16+O18*(D17-D16)/100","v":2.3600000000000003}]
[]
[]
[{"$nulls":12},"The value of the function at x0 = ",{"$nulls":3},{"$f":"P18","v":2.3600000000000003}]
[{"$nulls":13}," is   f ( x0)  = ",null,{"$f":"Sheet2!H2","v":{"v":0.09543581065645758,"d":"0.0954"}}]
["Click each item below for suggestions and investigations",{"$nulls":11},"The value of the curvature =",{"$nulls":3},{"$f":"Sheet2!H3","v":{"v":0.09339442730624366,"d":"0.0934"}}]
[null,"   Item 1",{"$nulls":10},"    and the radius of curvature =",{"$nulls":3},{"$f":"r0","v":{"v":10.707276963334914,"d":"10.71"}}]
[null,"   Item 2"]
[null,"   Item 3"]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["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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