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{"sheet":"Expo-Quad","index":0,"n_rows":30,"n_cols":18,"rows_kept":30,"merged":[[23,2,23,3]]}
[null,"Taylor Polynomials vs the Center:"]
["Quadratic Approximations to the Exponential Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  how the quadratic Taylor approximation"]
[null,null,"to the exponential function "]
[null,null,"              y = ex"]
[null,"        changes with the center point c."]
[]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":9},"The graph of the function y =",null,null,"ex"]
[null,null,"   Item 4"]
[{"$nulls":12},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"-2+dx*O22","v":2.41},"for the parabola"]
[]
[{"$nulls":14},147,{"$f":"#REF!+O22*dx","v":{"$error":"#REF!"}}]
["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":"Expo-Cubic","index":1,"n_rows":30,"n_cols":15,"rows_kept":30,"merged":[[23,2,23,3]]}
["       Taylor Polynomials vs the Center:"]
["   Cubic Approximations to the Exponential Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  how the quadratic Taylor approximation"]
[null,null,"to the exponential function "]
[{"$nulls":3},"y = ex"]
[null,"        changes with the center point c."]
[]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":6},"The graph of the function y =",null,null,"ex"]
[null,null,"   Item 4"]
[{"$nulls":9},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"-2+dx*L22","v":1.21},"for the cubic"]
[]
[{"$nulls":11},107,{"$f":"#REF!+L22*dx","v":{"$error":"#REF!"}}]
["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":"Sine-Linear","index":2,"n_rows":29,"n_cols":18,"rows_kept":29,"merged":[[22,2,22,3]]}
[null,"Taylor Polynomials vs the Center:"]
["        Linear Approximations to the Sine Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"     how the linear Taylor approximation"]
[null,null,"      to the sine function "]
[null,"        changes with the \"center\" point c."]
[]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4",{"$nulls":9},"The graph of the function y =",null,null,"sin x"]
[]
[{"$nulls":12},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"-PI()+dxx*O22","v":-0.9110618695410397},"for the line"]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":13},71,{"$f":"#REF!+O22*dx","v":{"$error":"#REF!"}}]
["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":"Sine-Cubic","index":3,"n_rows":29,"n_cols":16,"rows_kept":29,"merged":[[22,2,22,3]]}
[null,"Taylor Polynomials vs the Center:"]
["        Cubic Approximations to the Sine Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"     how the cubic Taylor approximation"]
[null,null,"      to the sine function "]
[null,"        changes with the \"center\" point c."]
[]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4",{"$nulls":7},"The graph of the function y =",null,null,"sin x"]
[]
[{"$nulls":10},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"-PI()+dxx*M22","v":0.7853981633974487},"for the cubic"]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":11},125,{"$f":"#REF!+M22*dx","v":{"$error":"#REF!"}}]
["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":"Cosine-Quad","index":4,"n_rows":27,"n_cols":16,"rows_kept":27,"merged":[[20,2,20,3]]}
[null,"Taylor Polynomials vs the Center:"]
["       Quadratic Approximations to the Cosine Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  how the quadratic Taylor approximation"]
[null,null,"    to the cosine function "]
[null,"        changes with the center point c."]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[{"$nulls":10},"The graph of the function y =",null,null,"cos x "]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":9},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"-PI()+dxx*M22","v":-0.7225663103256523},"for the parabola"]
["Click this link:",null,"DIGMath for Calculus"]
[{"$nulls":12},77,{"$f":"#REF!+M22*dx","v":{"$error":"#REF!"}}]
["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":"log-Quad","index":5,"n_rows":27,"n_cols":16,"rows_kept":27,"merged":[[20,2,20,3]]}
[null,"Taylor Polynomials vs the Center:"]
["  Quadratic Approximations to the Natural Log Function"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"  how the quadratic Taylor approximation"]
[null,"           to the natural logarithm function "]
[null,"          changes with the center point c."]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[]
[{"$nulls":10},"The graph of the function y =",null,null,"ln x "]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":9},"Select the center (point of tangency) x0 =",{"$nulls":3},{"$f":"0.1+dxxx*M22","v":0.19},"for the parabola"]
["Click this link:",null,"DIGMath for Calculus"]
[{"$nulls":12},10,{"$f":"#REF!+M22*dx","v":{"$error":"#REF!"}}]
["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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