■e^e (その2)

【1】4次近似

 a=2またはa=3として,テイラー展開

  exp(x)=exp(a){1+(x−a)+(x−a)^2/2+(x−a)^3/6+・・・}

の誤差項Rを1未満に抑えることを考える.

  R<exp(a)/n!<1

  n!>exp(a)

より,4次近似

  exp(x)=exp(a){1+(x−a)+(x−a)^2/2+(x−a)^3/6+(x−a)^4/24}

を採用したい.

[1]x=2.7,a=2 → 14.868

[2]x=2.7,a=3 → 14.8801

[3]x=2.8,a=2 → 16.4214

[4]x=2.8,a=3 → 16.4447

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【2】5次近似

  exp(x)=exp(a){1+(x−a)+(x−a)^2/2+(x−a)^3/6+(x−a)^4/24+(x−a)^5/120}

[1]x=2.7,a=2 → 14.8784

[2]x=2.7,a=3 → 14.8797

[3]x=2.8,a=2 → 16.4416

[4]x=2.8,a=3 → 16.4446

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【3】3次近似

  exp(x)=exp(a){1+(x−a)+(x−a)^2/2+(x−a)^3/6}

[1]x=2.7,a=2 → 14.7941

[2]x=2.7,a=3 → 14.8733

[3]x=2.8,a=2 → 16.2953

[4]x=2.8,a=3 → 16.4433

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【4】2次近似

  exp(x)=exp(a){1+(x−a)+(x−a)^2/2}

[1]x=2.7,a=2 → 14.3717

[2]x=2.7,a=3 → 14.9637

[3]x=2.8,a=2 → 15.6647

[4]x=2.8,a=3 → 16.4701

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【5】1次近似

  exp(x)=exp(a){1+(x−a)}

[1]x=2.7,a=2 → 12.5614

[2]x=2.7,a=3 → 14.0599

[3]x=2.8,a=2 → 13.3003

[4]x=2.8,a=3 → 16.0684

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