{"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 Sine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"  build the best linear approximation"]
[null,null,"     to the sine function"]
[{"$nulls":3},"y = sin x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the linear approximation sin x  » a0 + b0x "]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,104,null,null,{"$f":"(C19-0)/100-1","v":0.040000000000000036},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!H3:H203)","v":1.1307025731743114}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!I205","v":28.959793196420907}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":1}]
[]
["Your linear polynomial is y =",{"$nulls":3},{"$f":"TEXT(aa00,\"0.00\")&\" + \" &TEXT(bb00,\"0.00\")&\"x  \"","v":"0.04 + 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":37,"n_cols":15,"rows_kept":37}
[null,"Building Quadratic Approximations"]
[null,"        to the Sine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"build the best quadratic approximation"]
[null,null,"     to the sine function"]
[{"$nulls":3},"y = sin x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quadratic approximation sin x  » a0 + b0x + c0x2"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,0,null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!O3:O203)","v":3.1307025731743012}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!P205","v":250.4467676501941}]
[null,null,106,null,null,{"$f":"(C22-0)/100","v":1.06}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,48,null,null,{"$f":"(C25-0)/100","v":0.48}]
[]
["Your quadratic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a0,\"0.00\")&\" +\" &TEXT(b0,\"0.00\")&\"x  + \"&TEXT(c0,\"0.00\")&\"x^2\"","v":"0.00 +1.06x  + 0.48x^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 Sine Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"build the best cubic approximation"]
[null,null,"  to the sine function"]
[{"$nulls":3},"y = sin x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the cubic approximation sin x  » a0 + b0x + c0x2 + d0x3"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,92,null,null,{"v":0,"d":"0.00"},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!V3:V203)","v":5.77070257317428}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!W205","v":707.1736368473673}]
[null,null,82,null,null,{"$f":"(C22-0)/100","v":0.82}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C25-0)/100","v":{"v":0.5,"d":"0.50"}}]
[]
["What is the cubic coefficient d0  (-1 to 1)?"]
[null,null,138,null,null,{"$f":"(C28-0)/100-1","v":{"v":0.3799999999999999,"d":"0.38"}}]
[]
["Your cubic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a00,\"0.00\")&\" + \"&TEXT(b00,\"0.00\")&\"x + \"&TEXT(c00,\"0.00\")&\"x^2 + \"&TEXT(d00,\"0.00\")&\"x^3\"","v":"0.00 + 0.82x + 0.50x^2 + 0.38x^3"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$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 Sine Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"  build the best quartic approximation"]
[null,null,"  to the sine function"]
[{"$nulls":3},"y = sin x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quartic approximation sin x  » a0 + b0x + c0x2 + d0x3 + e0x4"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,92,null,null,{"v":0,"d":"0.00"},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!V3:V203)","v":5.77070257317428}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!W205","v":707.1736368473673}]
[null,null,82,null,null,{"$f":"(C22-0)/100","v":0.82}]
[]
["What is the quadratic coefficient c0  (0 to 2)?"]
[null,null,50,null,null,{"$f":"(C25-0)/100","v":{"v":0.5,"d":"0.50"}}]
[]
["What is the cubic coefficient d0  (-1 to 1)?"]
[null,null,41,null,null,{"$f":"(C28-0)/100-1","v":{"v":-0.5900000000000001,"d":"-0.59"}}]
[]
["What is the quartic coefficient e0  (-1 to 1)?"]
[null,null,41,null,null,{"$f":"(C31-0)/100-1","v":{"v":-0.5900000000000001,"d":"-0.59"}}]
[]
["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":"0.00 + 0.82x + 0.50x^2 + -0.59x^3 +-0.59x^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 Sine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"  build the best quintic approximation"]
[null,"               to the sine function"]
[{"$nulls":3},"y = sin x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quartic approximation sin x  » a0 + b0x + c0x2 + d0x3 + e0x4 + f0x5"]
[]
["What is the constant coefficient a0  (0 to 2)?"]
[null,null,100,null,null,{"v":0,"d":"0.00"},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!AI3:AI203)","v":0.26056366451729596}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!AK205","v":5059.285049281381}]
[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  (-1 to 1)?"]
[null,null,34,null,null,{"$f":"(C28-0)/200-1","v":-0.83}]
[]
["What is the quartic coefficient e0  (-1 to 1)?"]
[null,null,8,null,null,{"$f":"(C31-0)/200-1","v":-0.96}]
[]
["What is the quintic coefficient f0  (-0.2 to 0.2)?"]
[null,null,57,null,null,{"$f":"(C34-0)/250-0.2","v":{"v":0.027999999999999997,"d":"0.028"}}]
[]
["Your quintic polynomial is y =",{"$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,\"0.00\")&\"x^5  \"","v":"0.00 + 1.00x + 0.50x^2 + -0.83x^3 + -0.96x^4 + 0.03x^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":38,"rows_kept":205}
[{"$nulls":4},"Linear",{"$nulls":6},"Quadatic",{"$nulls":6},"Cubic",{"$nulls":6},"Quartic",{"$nulls":6},"Quintic"]
["Exponential ",null,null,"x","sin x","P1(x)","Difference","ABS","Squares",null,"x","sin x","P2(x)","Difference","ABS","Squares",null,"x","sin x","P3(x)","Difference","ABS","Squares",null,"x","sin x","P4(x)","Difference","ABS","Squares",null,"x","sin x","P5(x)","Difference","ABS","Squares"]
["y = e^x",null,null,{"$f":"a","v":-1},{"$f":"SIN(D3)","v":{"v":-0.8414709848078965,"d":"-0.84147"}},{"$f":"aa00+bb00*D3","v":{"v":-0.96,"d":"-0.96000"}},{"$f":"F3-E3","v":{"v":-0.11852901519210346,"d":"-0.11853"}},{"$f":"ABS(G3)","v":{"v":0.11852901519210346,"d":"0.11853"}},{"$f":"G3^2","v":{"v":0.014049127442409893,"d":"0.0140"}},null,{"$f":"a","v":-1},{"$f":"SIN(K3)","v":{"v":-0.8414709848078965,"d":"-0.84147"}},{"$f":"a0+b0*D3+c0*D3^2","v":{"v":-0.5800000000000001,"d":"-0.58000"}},{"$f":"M3-L3","v":{"v":0.26147098480789643,"d":"0.26147"}},{"$f":"ABS(N3)","v":{"v":0.26147098480789643,"d":"0.26147"}},{"$f":"N3^2","v":{"v":0.06836707589641121,"d":"0.0684"}},null,{"$f":"aa","v":-1},{"$f":"SIN(R3)","v":{"v":-0.8414709848078965,"d":"-0.84147"}},{"$f":"a00+b00*R3+c00*R3^2+d00*D3^3","v":{"v":-0.6999999999999998,"d":"-0.70000"}},{"$f":"T3-S3","v":{"v":0.14147098480789666,"d":"0.14147"}},{"$f":"ABS(U3)","v":{"v":0.14147098480789666,"d":"0.14147"}},{"$f":"U3^2","v":{"v":0.020014039542516127,"d":"0.0200"}},null,{"$f":"aaa","v":-1},{"$f":"SIN(Y3)","v":{"v":-0.8414709848078965,"d":"-0.84147"}},{"$f":"a000+b000*Y3+c000*Y3^2+d000*R3^3+e000*R3^4","v":{"v":-0.31999999999999995,"d":"-0.32000"}},{"$f":"AA3-Z3","v":{"v":0.5214709848078966,"d":"0.52147"}},{"$f":"ABS(AB3)","v":{"v":0.5214709848078966,"d":"0.52147"}},{"$f":"AB3^2","v":{"v":0.27193198799651747,"d":"0.2719"}},null,{"$f":"aaaa","v":-1},{"$f":"SIN(AF3)","v":{"v":-0.8414709848078965,"d":"-0.84147"}},{"$f":"a0000+b0000*AF3+c0000*AF3^2+d0000*AF3^3+e0000*AF3^4+f0000*AF3^5","v":{"v":-0.658,"d":"-0.65800"}},{"$f":"AH3-AG3","v":{"v":0.18347098480789648,"d":"0.18347"}},{"$f":"ABS(AI3)","v":{"v":0.18347098480789648,"d":"0.18347"}},{"$f":"AI3^2","v":{"v":0.03366160226637938,"d":"0.0337"}}]
[{"$f":"Quad!D12","v":-1},{"$f":"EXP(A4)","v":0.36787944117144233},null,{"$f":"D3+(b-a)/200","v":-0.985},{"$f":"SIN(D4)","v":{"v":-0.8332720904256761,"d":"-0.83327"}},{"v":-0.945,"d":"-0.94500"},{"$f":"F4-E4","v":{"v":-0.11172790957432388,"d":"-0.11173"}},{"$f":"ABS(G4)","v":{"v":0.11172790957432388,"d":"0.11173"}},{"$f":"G4^2","v":{"v":0.012483125777848294,"d":"0.0125"}},null,{"$f":"K3+(b-a)/200","v":-0.985},{"$f":"SIN(K4)","v":{"v":-0.8332720904256761,"d":"-0.83327"}},{"v":-0.578392,"d":"-0.57839"},{"$f":"M4-L4","v":{"v":0.25488009042567605,"d":"0.25488"}},{"$f":"ABS(N4)","v":{"v":0.25488009042567605,"d":"0.25488"}},{"$f":"N4^2","v":{"v":0.0649638604954008,"d":"0.0650"}},null,{"$f":"R3+(bb-aa)/200","v":-0.985},{"$f":"SIN(R4)","v":{"v":-0.8332720904256761,"d":"-0.83327"}},{"v":-0.6857427174999999,"d":"-0.68574"},{"$f":"T4-S4","v":{"v":0.14752937292567614,"d":"0.14753"}},{"$f":"ABS(U4)","v":{"v":0.14752937292567614,"d":"0.14753"}},{"$f":"U4^2","v":{"v":0.021764915875843224,"d":"0.0218"}},null,{"$f":"Y3+(bbb-aaa)/200","v":-0.985},{"$f":"SIN(Y4)","v":{"v":-0.8332720904256761,"d":"-0.83327"}},{"v":-0.31412980611875,"d":"-0.31413"},{"$f":"AA4-Z4","v":{"v":0.519142284306926,"d":"0.51914"}},{"$f":"ABS(AB4)","v":{"v":0.519142284306926,"d":"0.51914"}},{"$f":"AB4^2","v":{"v":0.26950871135541316,"d":"0.2695"}},null,{"$f":"AF3+(bbbb-aaaa)/200","v":-0.985},{"$f":"SIN(AF4)","v":{"v":-0.8332720904256761,"d":"-0.83327"}},{"v":-0.6363252019162375,"d":"-0.63633"},{"$f":"AH4-AG4","v":{"v":0.19694688850943853,"d":"0.19695"}},{"$f":"ABS(AI4)","v":{"v":0.19694688850943853,"d":"0.19695"}},{"$f":"AI4^2","v":{"v":0.03878807689354921,"d":"0.0388"}}]
[{"$f":"b","v":2},{"$f":"EXP(A5)","v":7.38905609893065},null,-0.97,{"v":-0.8248857133384501,"d":"-0.82489"},{"v":-0.9299999999999999,"d":"-0.93000"},{"v":-0.10511428666154987,"d":"-0.10511"},{"v":0.10511428666154987,"d":"0.10511"},{"v":0.011049013260366482,"d":"0.0110"},null,-0.97,{"v":-0.8248857133384501,"d":"-0.82489"},{"v":-0.576568,"d":"-0.57657"},{"v":0.2483177133384501,"d":"0.24832"},{"v":0.2483177133384501,"d":"0.24832"},{"v":0.061661686757636676,"d":"0.0617"},null,-0.97,{"v":-0.8248857133384501,"d":"-0.82489"},{"v":-0.6717657399999998,"d":"-0.67177"},{"v":0.1531199733384503,"d":"0.15312"},{"v":0.1531199733384503,"d":"0.15312"},{"v":0.023445726235167726,"d":"0.0234"},null,-0.97,{"v":-0.8248857133384501,"d":"-0.82489"},{"v":-0.30879568789999995,"d":"-0.30880"},{"v":0.5160900254384502,"d":"0.51609"},{"v":0.5160900254384502,"d":"0.51609"},{"v":0.26634891435706015,"d":"0.2663"},null,-0.97,{"v":-0.8248857133384501,"d":"-0.82489"},{"v":-0.6159570603196001,"d":"-0.61596"},{"v":0.20892865301885,"d":"0.20893"},{"v":0.20892865301885,"d":"0.20893"},{"v":0.04365118205227102,"d":"0.0437"}]
[{"$nulls":3},-0.955,{"v":-0.8163137404456834,"d":"-0.81631"},{"v":-0.9149999999999999,"d":"-0.91500"},{"v":-0.09868625955431654,"d":"-0.09869"},{"v":0.09868625955431654,"d":"0.09869"},{"v":0.009738977824821932,"d":"0.0097"},null,-0.955,{"v":-0.8163137404456834,"d":"-0.81631"},{"v":-0.5745279999999999,"d":"-0.57453"},{"v":0.24178574044568346,"d":"0.24179"},{"v":0.24178574044568346,"d":"0.24179"},{"v":0.058460344282867414,"d":"0.0585"},null,-0.955,{"v":-0.8163137404456834,"d":"-0.81631"},{"v":-0.6580613724999997,"d":"-0.65806"},{"v":0.15825236794568365,"d":"0.15825"},{"v":0.15825236794568365,"d":"0.15825"},{"v":0.02504381196041604,"d":"0.0250"},null,-0.955,{"v":-0.8163137404456834,"d":"-0.81631"},{"v":-0.3039628781187499,"d":"-0.30396"},{"v":0.5123508623269335,"d":"0.51235"},{"v":0.5123508623269335,"d":"0.51235"},{"v":0.26250340612715234,"d":"0.2625"},null,-0.955,{"v":-0.8163137404456834,"d":"-0.81631"},{"v":-0.5968309542707125,"d":"-0.59683"},{"v":0.21948278617497086,"d":"0.21948"},{"v":0.21948278617497086,"d":"0.21948"},{"v":0.04817269342712798,"d":"0.0482"}]
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