{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":1,"macros":1,"defined_names":5,"comments":1},"read":"whole","date_system":"1900"}

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["Taylor Approximations to Parametric Functions"]
[]
[null,"       This graphing utility produces the graphs"]
[null,"            of any parametric curve based on "]
[null,null,"    x = f(t)    and    y = g(t)"]
[null,"and the curve for the Taylor polynomials based on"]
[null,null,"   x = F(t)    and    y = G(t)"]
[null,"         on any interval from t = a  to t = b."]
[]
["Enter the first function in terms of t:   x = f(t) =  ",{"$nulls":4},"sin(t)"]
[]
["Enter the second function in terms of t:  y = g(t) = ",{"$nulls":4},"cos(t)"]
[]
["Enter the Taylor approximation to f in terms of t:    "]
[{"$nulls":4},"  x = F(t) =  ","t-t^3/6+t^5/120-t^7/5040"]
[]
["Enter the Taylor approximation to g in terms of t: "]
[{"$nulls":4},"  y = G(t) = ","1-t^2/2+t^4/24-t^6/720"]
[]
[]
["Now enter the interval for t :  "]
[null,"Starting value t = a =",null,-3.14]
[null,"Ending value t = b =",null,3.14,{"$nulls":4},"The graph of the parametric functions"]
[{"$nulls":9},"x =",{"$f":"F10","v":"sin(t)"}]
[{"$nulls":9},"y =",{"$f":"F12","v":"cos(t)"}]
[]
[{"$nulls":8},"Now trace along the parametric curve:"]
[{"$nulls":8},"t  = ",{"$f":"D22+K28*Sheet2!B12","v":{"v":-1.8739720558882236,"d":"-1.874"}},101]
["Click each item below for suggestions and investigations",{"$nulls":7},"x =",{"$f":"LOOKUP(J28,Sheet2!C3:C504,Sheet2!D3:D504)","v":{"v":-0.9543931811829954,"d":"-0.954"}}]
[null,"   Item 1",{"$nulls":6},"y =",{"$f":"LOOKUP(J28,Sheet2!C3:C504,Sheet2!E3:E504)","v":{"v":-0.29855260124708677,"d":"-0.299"}}]
[null,"   Item 2"]
[null,"   Item 3",{"$nulls":6},"Along the approximating Taylor functions:"]
[{"$nulls":8},"x =",{"$f":"LOOKUP($J28,Sheet2!C3:C503,Sheet2!F3:F503)","v":{"v":-0.9536322754554889,"d":"-0.954"}}]
[{"$nulls":8},"y =",{"$f":"LOOKUP(J28,Sheet2!C3:C503,Sheet2!G3:G503)","v":{"v":-0.30218136615335484,"d":"-0.302"}}]
[]
["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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[null,null,"t","x = f(t)","y = g(t)","x = F(t)","y =G(t)",null,null,"Tracing point"]
[]
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