L'Hospital's theorem - L'Hospital's theorem

Japanese: ロピタルの定理 - ろぴたるのていり（英語表記）L'Hospital's theorem

Assume that functions f and g are continuous in the closed interval [ a , b ], differentiable in the open interval ( a , b ), and g '( x ) does not become 0 in ( a , b ). If f ( a ) = g ( a ) = 0 exists, that is, if f ( a )/ g ( a ) is of the form 0/0, the limit value of the left side of (1) can be calculated by calculating the limit value of the right side of the equation obtained by separately differentiating the numerator and denominator. This is called the theorem of GFA de L'Hospital (1661-1704), or L'Hopital's rule. For example, it can be found as follows.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

関数f,gが閉区間[a,b]で連続，開区間(a,b)で微分可能，またg′(x)は(a,b)で0にならないとする。f(a)＝g(a)＝0であってが存在するならば，すなわちf(a)/g(a)が0/0の形のとき，(1)の左辺の極限値の計算は分母，分子を別々に微分した右辺の極限値を計算すればよい。これをロピタルG.F.A.de L’Hospital(1661‐1704)の定理，またはロピタルの法則という。例えば，と求められる。

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