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Direction

Limitおよび関連関数のオプションで，極限を取る方向を指定する．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
特性と関係  
関連項目
履歴
引用書式

Direction

Direction

Limitおよび関連関数のオプションで，極限を取る方向を指定する．

詳細

  • 次は，Directionの可能な設定である．
  • Reals または "TwoSided"両実数方向から
    "FromAbove" または -1上から，つまりより大きい値から
    "FromBelow" または +1下から，つまりより小さい値から
    Complexesすべての複素方向から
    Exp[ θ] の方向
    {dir1,…,dirn}変数 xiに方向 diriを独立で使う
  • x*におけるDirectionExp[ θ]は，極限値 x*に近付く曲線の接線方向を示す．

例題

すべて開く すべて閉じる

例  (1)

下からの極限：

Wolfram Language code: Limit[1 / x, x -> 0, Direction -> "FromBelow"]

上からの極限：

Wolfram Language code: Limit[1 / x, x -> 0, Direction -> "FromAbove"]

両側極限は存在しない：

Wolfram Language code: Limit[1 / x, x -> 0, Direction -> "TwoSided"]
Wolfram Language code: Plot[1 / x, {x, -1, 1}]

スコープ  (5)

区分ごとの不連続点における片側極限：

Wolfram Language code: Limit[RealAbs[x] / x, x -> 0, Direction -> "FromAbove"]
Wolfram Language code: Limit[RealAbs[x] / x, x -> 0, Direction -> "FromBelow"]

デフォルトの方向は両側である：

Wolfram Language code: Limit[RealAbs[x] / x, x -> 0]
Wolfram Language code: Plot[RealAbs[x] / x, {x, -1, 1}]

片側最大極限：

Wolfram Language code: MaxLimit[UnitStep[x]Sin[(1/x)] + (1/2), x -> 0, Direction -> "FromAbove"]
Wolfram Language code: MaxLimit[UnitStep[x]Sin[(1/x)] + (1/2), x -> 0, Direction -> "FromBelow"]

デフォルトの方向Realsは，2つの片側最大極限の大きい方を与える：

Wolfram Language code: MaxLimit[UnitStep[x]Sin[(1/x)] + (1/2), x -> 0]
Wolfram Language code: MaxLimit[UnitStep[x]Sin[(1/x)] + (1/2), x -> 0, Direction -> Reals]

関数を可視化する：

Wolfram Language code: Plot[UnitStep[x]Sin[(1/x)] + (1/2), {x, -.1, .1}]

単純極における極限：

Wolfram Language code: Limit[Tan[x], x -> π / 2, Direction -> "FromBelow"]
Wolfram Language code: Limit[Tan[x], x -> π / 2, Direction -> "FromAbove"]
Wolfram Language code: Limit[Tan[x], x -> π / 2, Direction -> ℝ]
Wolfram Language code: Limit[Tan[x], x -> π / 2, Direction -> ℂ]

分枝切断線における極限：

Wolfram Language code: Limit[Sqrt[x], x -> -1, Direction -> Reals]
Wolfram Language code: Limit[Sqrt[x], x -> -1, Direction -> -I]
Wolfram Language code: Limit[Sqrt[x], x -> -1, Direction -> +I]
Wolfram Language code: Limit[Sqrt[x], x -> -1, Direction -> Complexes]

別々の象限から近付く二変量極限を計算する：

Wolfram Language code: f[x_, y_] := (x y/x + y)(2 + RealSign[ x y] + RealSign[y])

第1象限から原点に近付く：

Wolfram Language code: Limit[f[x, y], {x, y} -> {0, 0}, Direction -> "FromAbove"]

同様に：

Wolfram Language code: Limit[f[x, y], {x, y} -> {0, 0}, Direction -> {"FromAbove", "FromAbove"}]

第2象限から原点に近付く：

Wolfram Language code: Limit[f[x, y], {x, y} -> {0, 0}, Direction -> {"FromBelow", "FromAbove"}]

左半平面から原点に近付く：

Wolfram Language code: Limit[f[x, y], {x, y} -> {0, 0}, Direction -> {"FromBelow", Reals}]

下半平面から原点に近付く：

Wolfram Language code: Limit[f[x, y], {x, y} -> {0, 0}, Direction -> {Reals, "FromBelow"}]

関数を可視化する：

Wolfram Language code: Row@{Plot3D[f[x, y], {x, y}∈Disk[], Exclusions -> {{x == -y , x <= 0}}, ClippingStyle -> None, ImageSize -> 200], DensityPlot[f[x, y], {x, -1, 1}, {y, -1, 1}, Exclusions -> {{x == -y , x <= 0}}, ClippingStyle -> Automatic, ImageSize -> Small]}

特性と関係  (4)

"FromBelow"と1の設定は等しい：

Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> "FromBelow"]
Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> 1]

"FromAbove"と-1の設定は等しい：

Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> "FromAbove"]
Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> -1]

"TwoSided"とRealsの設定は等しい：

Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> "TwoSided"]
Wolfram Language code: MinLimit[Cos[x] / x, x -> 0, Direction -> ℝ]

Directionは極限変数に制約条件を加える：

Wolfram Language code: Limit[Tan[x], x -> π / 2 + n π, Direction -> 1, Assumptions -> n∈Integers]

極限の式でパラメータにAssumptionsを適用する：

Wolfram Language code: Limit[Tan[x], x -> π / 2 + n π, Direction -> -1, Assumptions -> n∈Integers]
Wolfram Language code: Plot[Tan[x], {x, -2π, 2π}, ExclusionsStyle -> {{Dashed, Red}}]
Wolfram Research (1991), Direction, Wolfram言語関数， https://reference.wolfram.com/language/ref/Direction.html （2017年に更新）.

テキスト

Wolfram Research (1991), Direction, Wolfram言語関数， https://reference.wolfram.com/language/ref/Direction.html （2017年に更新）.

CMS

Wolfram Language. 1991. "Direction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Direction.html.

APA

Wolfram Language. (1991). Direction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Direction.html

BibTeX

@misc{reference.wolfram_2026_direction, author="Wolfram Research", title="{Direction}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Direction.html}", note=[Accessed: 14-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_direction, organization={Wolfram Research}, title={Direction}, year={2017}, url={https://reference.wolfram.com/language/ref/Direction.html}, note=[Accessed: 14-September-2026]}