improper code - перевод на Английский
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improper code - перевод на Английский

LIMIT OF A DEFINITE INTEGRAL WITH AS ONE OR BOTH LIMITS APPROACH INFINITY OR VALUES AT WHICH THE INTEGRAND IS UNDEFINED
Improper Riemann integral; Improper integrals; Improper Integrals
  • The improper integral<br/><math>\int_{0}^{\infty} \frac{dx}{(x+1)\sqrt{x}} = \pi</math><br/> has unbounded intervals for both domain and range.
  • The improper integral<br/><math>\int_{-1}^{1} \frac{dx}{\sqrt[3]{x^2}} = 6</math><br/> converges, since both left and right limits exist, though the integrand is unbounded near an interior point.
  • An improper Riemann integral of the second kind. The integral may fail to exist because of a [[vertical asymptote]] in the function.
  • Figure 1
  • An improper integral of the first kind. The integral may need to be defined on an unbounded domain.
  • Figure 2

improper code      
(illegal code) неразрешенный (несанкционированный) код
codetext         
  • A portion of the "[[Zimmermann Telegram]]" as decrypted by [[British Naval Intelligence]] codebreakers. The word ''Arizona'' was not in the German codebook and had therefore to be split into phonetic syllables.
METHOD USED TO ENCRYPT A MESSAGE
Codetext; Idiot code; One-part code; Two-part code; Cryptography code
(за) кодированный текст
Napoleonic Code         
  • The Napoleonic Code in the [[Historical Museum of the Palatinate]] in [[Speyer]]
CIVIL CODE OF 1804
Code Napoleon; Napoleonic civil code; Napoleanic Code; Code Civil; Code Napoléon; French Familly code; Code civil; French Civil Code; Civil Code of France; Civil Code of 1804; French civil code; Code civil du Français; Napoleonic law; Code civil des Français; Code civil des Francais; Napoleonic code; Napoléonic Code; Code Civil des Francais; Code Civil of 1804; French Napoleonic Code of 1804
[юр.] кодекс Наполеона

Определение

ФРАНЦУЗСКИЙ ГРАЖДАНСКИЙ КОДЕКС
1804 (Кодекс Наполеона) , действующий гражданский кодекс Франции. Составлен при активном участии Наполеона. Включает нормы гражданского, семейного, процессуального, частично трудового права. Кодекс закрепил свободу частной собственности, провозгласив это право священным и неприкосновенным.

Википедия

Improper integral

In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or positive or negative infinity; or in some instances as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, in some cases with infinity as a limit of integration interval(s).

Specifically, an improper integral is a limit of the form:

lim b a b f ( x ) d x , lim a a b f ( x ) d x {\displaystyle \lim _{b\to \infty }\int _{a}^{b}f(x)\,dx,\quad \lim _{a\to -\infty }\int _{a}^{b}f(x)\,dx}

or

lim c b a c f ( x )   d x , lim c a + c b f ( x )   d x {\displaystyle \lim _{c\to b^{-}}\int _{a}^{c}f(x)\ dx,\quad \lim _{c\to a^{+}}\int _{c}^{b}f(x)\ dx}

where in each case one takes a limit in one of integration endpoints (Apostol 1967, §10.23). Of course, limits in both endpoints are also possible and this case is also considered as an improper integral.

By abuse of notation, improper integrals are often written symbolically just like standard definite integrals, perhaps with infinity among the limits of integration interval(s). When the definite integral exists (in the sense of either the Riemann integral or the more powerful Lebesgue integral), this ambiguity is resolved as both the proper and improper integral will coincide in value.

The purpose of using improper integrals is that one is often able to compute values for improper integrals, even when the function is not integrable in the conventional sense (as a Riemann integral, for instance) because of a singularity in the function as an integrand or because one of the bounds of integration is infinite.

Как переводится improper code на Русский язык