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{"sheet":"平均変化率","index":0,"n_rows":25,"n_cols":15,"rows_kept":25,"cut":false,"hidden":false,"merged":[[0,0,0,4]],"flags":["formulas_cached_only"]}
["y=f(x)=x2のx=aにおける微分係数を求める"]
[{"$nulls":9},"h","x=a+h","y=f(a)+Δy","Δy=y-f(a)","平均変化率"]
["たとえば",null,"そのときの",{"$nulls":6},"hはa=1からの増加分","xはa=1+hで求める","y=x2で計算","Δyはyとf(a)=1との引き算","(y-f(a)）/h"]
["a＝",1,"f(a)=",1,{"$nulls":5},1,2,4,3,3]
[null,"↑数字を入れると平均変化率の変化状況は右表で計算される。",{"$nulls":7},0.5,1.5,2.25,1.25,2.5]
[{"$nulls":9},0.25,1.25,1.5625,0.5625,2.25]
[{"$nulls":6},"平均変化率",null,null,0.125,1.125,1.265625,0.265625,2.125]
[{"$nulls":9},0.0625,1.0625,1.12890625,0.12890625,2.0625]
[{"$nulls":9},0.03125,1.03125,1.0634765625,0.0634765625,2.03125]
[{"$nulls":9},0.015625,1.015625,1.031494140625,0.031494140625,2.015625]
[{"$nulls":9},0.0078125,1.0078125,1.01568603515625,0.01568603515625,2.0078125]
[{"$nulls":6},"y=f(x)のx=aにおける微分係数",null,null,0.00390625,1.00390625,1.0078277587890625,0.0078277587890625,2.00390625]
[{"$nulls":9},0.001953125,1.001953125,1.0039100646972656,0.003910064697265625,2.001953125]
[{"$nulls":9},0.0009765625,1.0009765625,1.0019540786743164,0.0019540786743164062,2.0009765625,"←プラスから接線に近づく"]
[{"$nulls":9},-0.0009765625,0.9990234375,0.9980478286743164,-0.0019521713256835938,1.9990234375,"←マイナスから接線に近づく"]
[{"$nulls":9},-0.001953125,0.998046875,0.9960975646972656,-0.003902435302734375,1.998046875]
[{"$nulls":9},-0.00390625,0.99609375,0.9922027587890625,-0.0077972412109375,1.99609375]
[{"$nulls":9},-0.0078125,0.9921875,0.98443603515625,-0.01556396484375,1.9921875]
[{"$nulls":9},-0.015625,0.984375,0.968994140625,-0.031005859375,1.984375]
[{"$nulls":9},-0.03125,0.96875,0.9384765625,-0.0615234375,1.96875]
[{"$nulls":9},-0.0625,0.9375,0.87890625,-0.12109375,1.9375]
[{"$nulls":9},-0.125,0.875,0.765625,-0.234375,1.875]
[{"$nulls":9},-0.25,0.75,0.5625,-0.4375,1.75]
[{"$nulls":9},-0.5,0.5,0.25,-0.75,1.5]
[{"$nulls":9},-1,0,0,-1,1]

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["y=f(x)=x2のx=aにおける傾きを求める"]
[{"$nulls":8},"↓x = a の近辺の値を入力、aに近づくほど差がなくなる"]
["接点のx",null,1,"接点のy",1,null,"別の点のx",null,0.95,"別の点のy",0.9025]
["接点における傾き"]
[null,"Δy/Δx=f'(a)=2a=",2,null,null,null,"このときの傾き\nΔy/Δx",null,1.9499999999999988]
[{"$nulls":9},"この式から2つのy座標を求める"]
[{"$nulls":9},"y=Δy/Δx・(x-a)+b"]
[{"$nulls":9},"↓","↓"]
[{"$nulls":7},"x","y=x2","接線のy座標","接点と別の点を結んだ線のy座標","y座標の差"]
[{"$nulls":7},-3,9,-7,-6.799999999999995,-0.20000000000000462]
[{"$nulls":7},-2.8,7.839999999999999,-6.6,-6.409999999999996,-0.19000000000000394]
[{"$nulls":7},-2.6,6.760000000000001,-6.2,-6.019999999999996,-0.18000000000000416]
[{"$nulls":7},-2.4,5.76,-5.8,-5.629999999999996,-0.17000000000000348]
[{"$nulls":7},-2.2,4.840000000000001,-5.4,-5.239999999999997,-0.1600000000000037]
[{"$nulls":7},-2,4,-5,-4.849999999999996,-0.1500000000000039]
[{"$nulls":7},-1.8,3.24,-4.6,-4.459999999999996,-0.14000000000000323]
[{"$nulls":7},-1.6,2.5600000000000005,-4.2,-4.069999999999997,-0.13000000000000345]
[{"$nulls":7},-1.4,1.9599999999999997,-3.8,-3.679999999999997,-0.12000000000000277]
[{"$nulls":7},-1.2,1.44,-3.4000000000000004,-3.2899999999999974,-0.11000000000000298]
[{"$nulls":7},-1,1,-3,-2.8999999999999977,-0.10000000000000231]
[{"$nulls":7},-0.8,0.6400000000000001,-2.6,-2.509999999999998,-0.09000000000000208]
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[{"$nulls":7},-0.4,0.16000000000000003,-1.7999999999999998,-1.7299999999999982,-0.07000000000000162]
[{"$nulls":7},-0.2,0.04000000000000001,-1.4,-1.3399999999999985,-0.060000000000001386]
[{"$nulls":7},0,0,-1,-0.9499999999999988,-0.050000000000001155]
[{"$nulls":7},0.2,0.04000000000000001,-0.6000000000000001,-0.5599999999999992,-0.040000000000000924]
[{"$nulls":7},0.4,0.16000000000000003,-0.19999999999999996,-0.16999999999999926,-0.030000000000000693]
[{"$nulls":7},0.6,0.36,0.19999999999999996,0.22000000000000042,-0.020000000000000462]
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[{"$nulls":7},1,1,1,1,0]
[{"$nulls":7},1.2,1.44,1.4,1.3899999999999997,0.010000000000000231]
[{"$nulls":7},1.4,1.9599999999999997,1.7999999999999998,1.7799999999999994,0.020000000000000462]
[{"$nulls":7},1.6,2.5600000000000005,2.2,2.1699999999999995,0.030000000000000693]
[{"$nulls":7},1.8,3.24,2.6,2.559999999999999,0.040000000000000924]
[{"$nulls":7},2,4,3,2.949999999999999,0.050000000000001155]
[{"$nulls":7},2.2,4.840000000000001,3.4000000000000004,3.339999999999999,0.060000000000001386]
[{"$nulls":7},2.4,5.76,3.8,3.729999999999998,0.07000000000000162]
[{"$nulls":7},2.6,6.760000000000001,4.2,4.119999999999998,0.08000000000000185]
[{"$nulls":7},2.8,7.839999999999999,4.6,4.509999999999998,0.09000000000000163]
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["3次関数　y1=(x+1)3/6 \nと y2=-x3/2+x2/2+ｘ/2+1/6 のグラフ"]
[{"$nulls":6},"x","y1（-2≦x≦2）","y2（-2≦x≦2）"]
[{"$nulls":6},-2,-0.16666666666666666,5.166666666666667]
[{"$nulls":6},-1.5,-0.020833333333333332,2.2291666666666665]
[{"$nulls":6},-1,0,0.6666666666666666]
[{"$nulls":6},-0.5,0.020833333333333332,0.10416666666666666]
[{"$nulls":6},0,0.16666666666666666,0.16666666666666666,"一致"]
[{"$nulls":6},0.5,0.5625,0.47916666666666663]
[{"$nulls":6},1,1.3333333333333333,0.6666666666666666]
[{"$nulls":6},1.5,2.6041666666666665,0.35416666666666663]
[{"$nulls":6},1.7024,3.2892557783039997,3.08517546669107e-05]
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