{"text_format":"3","workbook":"xlsx","n_sheets":6,"sheets":["Linear","Quad","Cubic","Quartic","Quintic","Calcs"],"not_rendered":{"charts":5,"macros":1,"external_links":1,"defined_names":46,"comments":5},"read":"whole","date_system":"1900"}

{"sheet":"Linear","index":0,"n_rows":33,"n_cols":15,"rows_kept":33}
[null,"Building Linear Approximations"]
[null,"    to the Exponential Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"  build the best linear approximation"]
[null,null,"to the exponential function"]
[{"$nulls":3},"y = ex"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",1]
[]
[]
["In the linear approximation ex » a0 + b0x "]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100","v":1},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!E3:E203)","v":0.7182818284590473}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!F205","v":12.448530104814457}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":1}]
[]
["Your linear polynomial is y =",{"$nulls":3},{"$f":"TEXT(aa00,\"0.00\")&\" + \" &TEXT(bb00,\"0.00\")&\"x  \"","v":"1.00 + 1.00x  "}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]

{"sheet":"Quad","index":1,"n_rows":36,"n_cols":15,"rows_kept":36}
[null,"Building Quadratic Approximations"]
[null,"    to the Exponential Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"build the best quadratic approximation"]
[null,null,"to the exponential function"]
[{"$nulls":3},"y = ex"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",1]
[]
["In the quadratic approximation ex » a0 + b0x + c0x2"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"$f":"(C18-0)/100","v":1},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!L3:L203)","v":0.21828182845904598}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!M205","v":0.9315516376125513}]
[null,null,100,null,null,{"$f":"(C21-0)/100","v":1}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C24-0)/100","v":0.5}]
[]
["Your quadratic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a0,\"0.00\")&\" +\" &TEXT(b0,\"0.00\")&\"x  + \"&TEXT(c0,\"0.00\")&\"x^2\"","v":"1.00 +1.00x  + 0.50x^2"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[{"$nulls":3},"   Item 5"]

{"sheet":"Cubic","index":2,"n_rows":40,"n_cols":15,"rows_kept":40}
[null,"  Building Cubic Approximations"]
[null,"    to the Exponential Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"build the best cubic approximation"]
[null,"       to the exponential function"]
[{"$nulls":3},"y = ex"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",1]
[]
[]
["In the cubic approximation ex » a0 + b0x + c0x2 + d0x3"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100","v":{"v":1,"d":"1.00"}},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!S3:S203)","v":0.04828182845904516}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!T205","v":0.04302927975427065}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":{"v":1,"d":"1.00"}}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C25-0)/100","v":{"v":0.5,"d":"0.50"}}]
[]
["What is the cubic coefficient d0  (0 to 1)?"]
[null,null,17,null,null,{"$f":"(C28-0)/100","v":0.17}]
[]
["Your cubic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a00,\"0.00\")&\" + \"&TEXT(b00,\"0.00\")&\"x + \"&TEXT(c00,\"0.00\")&\"x^2 + \"&TEXT(d00,\"0.00\")&\"x^3\"","v":"1.00 + 1.00x + 0.50x^2 + 0.17x^3"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[{"$nulls":3},"   Item 5"]

{"sheet":"Quartic","index":3,"n_rows":43,"n_cols":15,"rows_kept":43}
[null,"Building Quartic Approximations"]
[null,"    to the Exponential Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"  build the best quartic approximation"]
[null,"       to the exponential function"]
[{"$nulls":3},"y = ex"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",1]
[]
[]
["In the quartic approximation ex » a0 + b0x + c0x2 + d0x3 + e0x4"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100","v":{"v":1,"d":"1.00"}},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!Z3:Z203)","v":0.008281828459045126}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!AA205","v":5.8828616342216278E-4}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":{"v":1,"d":"1.00"}}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C25-0)/100","v":{"v":0.5,"d":"0.50"}}]
[]
["What is the cubic coefficient d0  (0 to 1)?"]
[null,null,17,null,null,{"$f":"(C28-0)/100","v":0.17}]
[]
["What is the quartic coefficient e0  (0 to 1)?"]
[null,null,4,null,null,{"$f":"(C31-0)/100","v":0.04}]
[]
["Your quartic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a000,\"0.00\")&\" + \"&TEXT(b000,\"0.00\")&\"x + \"&TEXT(c000,\"0.00\")&\"x^2 + \"&TEXT(d000,\"0.00\")&\"x^3 +\"&TEXT(e000,\"0.00\")&\"x^4\"","v":"1.00 + 1.00x + 0.50x^2 + 0.17x^3 +0.04x^4"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]

{"sheet":"Quintic","index":4,"n_rows":47,"n_cols":15,"rows_kept":47}
[null,"Building Quintic Approximations"]
[null,"    to the Exponential Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"  build the best quintic approximation"]
[null,"       to the exponential function"]
[{"$nulls":3},"y = ex"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",1]
[]
[]
["In the quintic approximation ex » a0 + b0x + c0x2 + d0x3 + e0x4"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100","v":{"v":1,"d":"1.00"}},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!AF3:AF203)","v":0.7697181715409589}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!AH205","v":7.7409354236190495}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":{"v":1,"d":"1.00"}}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C25-0)/100","v":{"v":0.5,"d":"0.50"}}]
[]
["What is the cubic coefficient d0  (0 to 1)?"]
[null,null,97,null,null,{"$f":"(C28-0)/200","v":{"v":0.485,"d":"0.49"}}]
[]
["What is the quartic coefficient e0  (0 to 1)?"]
[null,null,99,null,null,{"$f":"(C31-0)/200","v":{"v":0.495,"d":"0.50"}}]
[]
["What is the quintic coefficient f0  (0 to 0.2)?"]
[null,null,40,null,null,{"$f":"(C34-0)/5000","v":{"v":0.008,"d":"0.0080"}}]
[]
["Your quintic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a0000,\"0.00\")&\" + \"&TEXT(b0000,\"0.00\")&\"x + \"&TEXT(c0000,\"0.00\")&\"x^2 + \"&TEXT(d0000,\"0.00\")&\"x^3 + \"&TEXT(e0000,\"0.00\")&\"x^4 + \"&TEXT(f0000,\"0.0000\")&\"x^5  \"","v":"1.00 + 1.00x + 0.50x^2 + 0.49x^3 + 0.50x^4 + 0.0080x^5  "}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]
[null,null,"   Item 6"]

{"sheet":"Calcs","index":5,"n_rows":205,"n_cols":35,"rows_kept":205}
[null,"Linear",{"$nulls":6},"Quadatic",{"$nulls":6},"Cubic",{"$nulls":6},"Quartic",{"$nulls":6},"Quintic"]
["x","e^x","P1(x)","Difference","ABS","Squares",null,"x","e^x","P2(x)","Difference","ABS","Squares",null,"x","e^x","P3(x)","Difference","ABS","Squares",null,"x","e^x","P4(x)","Difference","ABS","Squares",null,"x","e^x","P5(x)","Difference","ABS","Squares"]
[{"$f":"aa0","v":-1},{"$f":"EXP(A3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"aa00+bb00*A3","v":{"v":0,"d":"0.00000"}},{"$f":"C3-B3","v":{"v":-0.36787944117144233,"d":"-0.36788"}},{"$f":"ABS(D3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"D3^2","v":{"v":0.1353352832366127,"d":"0.1353"}},null,{"$f":"a","v":-1},{"$f":"EXP(H3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"a0+b0*H3+c0*H3^2","v":{"v":0.5,"d":"0.50000"}},{"$f":"J3-I3","v":{"v":0.13212055882855767,"d":"0.13212"}},{"$f":"ABS(K3)","v":{"v":0.13212055882855767,"d":"0.13212"}},{"$f":"K3^2","v":{"v":0.01745584206517037,"d":"0.0175"}},null,{"$f":"aa","v":-1},{"$f":"EXP(O3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"a00+b00*O3+c00*O3^2+d00*A3^3","v":{"v":0.32999999999999996,"d":"0.33000"}},{"$f":"Q3-P3","v":{"v":-0.037879441171442374,"d":"-0.03788"}},{"$f":"ABS(R3)","v":{"v":0.037879441171442374,"d":"0.03788"}},{"$f":"R3^2","v":{"v":1.4348520634607637E-3,"d":"0.0014"}},null,{"$f":"aaa","v":-1},{"$f":"EXP(V3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"a000+b000*V3+c000*V3^2+d000*O3^3+e000*O3^4","v":{"v":0.36999999999999994,"d":"0.37000"}},{"$f":"X3-W3","v":{"v":2.120558828557606E-3,"d":"0.00212"}},{"$f":"ABS(Y3)","v":{"v":2.120558828557606E-3,"d":"0.00212"}},{"$f":"Y3^2","v":{"v":4.4967697453736065E-6,"d":"0.0000"}},null,{"$f":"aaaa","v":-1},{"$f":"EXP(AC3)","v":{"v":0.36787944117144233,"d":"0.36788"}},{"$f":"a0000+b0000*AC3+c0000*AC3^2+d0000*AC3^3+e0000*AC3^4+f0000*AC3^5","v":{"v":0.502,"d":"0.50200"}},{"$f":"AE3-AD3","v":{"v":0.13412055882855767,"d":"0.13412"}},{"$f":"ABS(AF3)","v":{"v":0.13412055882855767,"d":"0.13412"}},{"$f":"AF3^2","v":{"v":0.0179883243004846,"d":"0.0180"}}]
[{"$f":"A3+(bb0-aa0)/200","v":-0.99},{"$f":"EXP(A4)","v":{"v":0.3715766910220457,"d":"0.37158"}},{"v":0.010000000000000009,"d":"0.01000"},{"$f":"C4-B4","v":{"v":-0.3615766910220457,"d":"-0.36158"}},{"$f":"ABS(D4)","v":{"v":0.3615766910220457,"d":"0.36158"}},{"$f":"D4^2","v":{"v":0.1307377034904519,"d":"0.1307"}},null,{"$f":"H3+(b-a)/200","v":-0.99},{"$f":"EXP(H4)","v":{"v":0.3715766910220457,"d":"0.37158"}},0.50005,{"$f":"J4-I4","v":{"v":0.12847330897795428,"d":"0.12847"}},{"$f":"ABS(K4)","v":{"v":0.12847330897795428,"d":"0.12847"}},{"$f":"K4^2","v":{"v":0.01650539111974491,"d":"0.0165"}},null,{"$f":"O3+(bb-aa)/200","v":-0.99},{"$f":"EXP(O4)","v":{"v":0.3715766910220457,"d":"0.37158"}},{"v":0.33509917,"d":"0.33510"},{"$f":"Q4-P4","v":{"v":-0.03647752102204571,"d":"-0.03648"}},{"$f":"ABS(R4)","v":{"v":0.03647752102204571,"d":"0.03648"}},{"$f":"R4^2","v":{"v":1.3306095399137868E-3,"d":"0.0013"}},null,{"$f":"V3+(bbb-aaa)/200","v":-0.99},{"$f":"EXP(V4)","v":{"v":0.3715766910220457,"d":"0.37158"}},{"v":0.3735230104,"d":"0.37352"},{"$f":"X4-W4","v":{"v":1.9463193779543086E-3,"d":"0.00195"}},{"$f":"ABS(Y4)","v":{"v":1.9463193779543086E-3,"d":"0.00195"}},{"$f":"Y4^2","v":{"v":3.7881591210004471E-6,"d":"0.0000"}},null,{"$f":"AC3+(bbbb-aaaa)/200","v":-0.99},{"$f":"EXP(AC4)","v":{"v":0.3715766910220457,"d":"0.37158"}},{"v":0.49734208955079995,"d":"0.49734"},{"$f":"AE4-AD4","v":{"v":0.12576539852875424,"d":"0.12577"}},{"$f":"ABS(AF4)","v":{"v":0.12576539852875424,"d":"0.12577"}},{"$f":"AF4^2","v":{"v":0.01581693546709638,"d":"0.0158"}}]
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