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© Copyright 2023, Maciej Szeptuch. Created using Sphinx 4.2.0.
Ewentualne błędy proszę zgłąszać w Repozytorium GitHub

-Tue Jan 23 09:58:33 2024 +0100 update exam date (c9d12d1b97cfe6faca36120afca7f2d70f131299) +Sat Jan 27 17:28:55 2024 +0100 matematyka_cw: add useful notes (989558f1356b24bb0d4bbefdb632db45524bfd40) diff --git a/assets/links.html b/assets/links.html index 004d0dd2..1aca2331 100644 --- a/assets/links.html +++ b/assets/links.html @@ -132,7 +132,7 @@

Nawigacja

© Copyright 2023, Maciej Szeptuch. Created using Sphinx 4.2.0.
Ewentualne błędy proszę zgłąszać w Repozytorium GitHub

-Tue Jan 23 09:58:33 2024 +0100 update exam date (c9d12d1b97cfe6faca36120afca7f2d70f131299) +Sat Jan 27 17:28:55 2024 +0100 matematyka_cw: add useful notes (989558f1356b24bb0d4bbefdb632db45524bfd40) diff --git a/assets/notes/algebra.html b/assets/notes/algebra.html index 461e84ac..15700c7a 100644 --- a/assets/notes/algebra.html +++ b/assets/notes/algebra.html @@ -1351,7 +1351,7 @@

Nawigacja

© Copyright 2023, Maciej Szeptuch. Created using Sphinx 4.2.0.
Ewentualne błędy proszę zgłąszać w Repozytorium GitHub

-Tue Jan 23 09:58:33 2024 +0100 update exam date (c9d12d1b97cfe6faca36120afca7f2d70f131299) +Sat Jan 27 17:28:55 2024 +0100 matematyka_cw: add useful notes (989558f1356b24bb0d4bbefdb632db45524bfd40) diff --git a/assets/notes/algebra/algebra_2023.10.09.html b/assets/notes/algebra/algebra_2023.10.09.html index 3b08224a..fdfdab79 100644 --- a/assets/notes/algebra/algebra_2023.10.09.html +++ b/assets/notes/algebra/algebra_2023.10.09.html @@ -180,7 +180,7 @@

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-Tue Jan 23 09:58:33 2024 +0100 update exam date (c9d12d1b97cfe6faca36120afca7f2d70f131299) +Sat Jan 27 17:28:55 2024 +0100 matematyka_cw: add useful notes (989558f1356b24bb0d4bbefdb632db45524bfd40) diff --git a/assets/notes/matematyka_cw/matematyka_cw_2024.01.25.html b/assets/notes/matematyka_cw/matematyka_cw_2024.01.25.html new file mode 100644 index 00000000..fde090e8 --- /dev/null +++ b/assets/notes/matematyka_cw/matematyka_cw_2024.01.25.html @@ -0,0 +1,132 @@ + + + + + + + + + + <no title> — Matematyka - dokumentacja + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Objętość bryły utworozonej przez krzywą obracaną wokół osi OX: \(|V| = \pi \int_a^b f^2(x)dx\)

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Pole powierzchni figury utworzonej poprzez obrut prostej f(x) wokół osi x \(|S| = \int_a^b f(x) * \sqrt{1+f'(x)^2}\)

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+© Copyright 2023, Maciej Szeptuch. +Created using Sphinx 4.2.0.
+Ewentualne błędy proszę zgłąszać w Repozytorium GitHub

+Sat Jan 27 17:28:55 2024 +0100 matematyka_cw: add useful notes (989558f1356b24bb0d4bbefdb632db45524bfd40) + + + + \ No newline at end of file diff --git a/assets/notes/matematyka_cw/matematyka_cw_2024.01.27.html b/assets/notes/matematyka_cw/matematyka_cw_2024.01.27.html new file mode 100644 index 00000000..62ad905f --- /dev/null +++ b/assets/notes/matematyka_cw/matematyka_cw_2024.01.27.html @@ -0,0 +1,179 @@ + + + + + + + + + + Granice: - Tricki — Matematyka - dokumentacja + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Granice: - Tricki¶

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Symbole Nieoznaczone czyli co z tym robić?¶

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\(0 * \infty\)¶

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+\[ +\left[0 * \infty\right] = +\left[\frac{0}{\frac{1}{\infty}}\right] = +\left[\frac{0}{0}\right] +\]
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Teraz można użyć twierdzenia de l’Hospital.

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Dowód:

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+\[\begin{split} +\lim_{n \to \infty} n \frac{1}{n^2} \stackrel{\left[0 * \infty\right]}{=} 0 \\ +\lim_{n \to \infty} n^2 \frac{1}{n} \stackrel{\left[0 * \infty\right]}{=} \infty \\ +\end{split}\]
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\(\infty - \infty\)¶

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Dowód:

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+\[\begin{split} +\lim_{n \to \infty} n - n^2 \stackrel{\left[\infty - \infty\right]}{=} \lim_{n\to \infty} n^2(\frac{1}{n} - 1) = - \infty \\ +\lim_{n \to \infty} n^2 - n \stackrel{\left[\infty - \infty\right]}{=} \lim_{n\to \infty} n^2(1-\frac{1}{n}) = \infty \\ +\end{split}\]
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+
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\(\frac{\infty}{\infty}\) i \(\frac{0}{0}\)¶

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Dowód analogiczny jak powyżej. Aby rozwiązać korzystamy z twierdzenia de l’Hospital’a

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+© Copyright 2023, Maciej Szeptuch. +Created using Sphinx 4.2.0.
+Ewentualne błędy proszę zgłąszać w Repozytorium GitHub

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[20, "wazne-granice"]], "Funkcje ci\u0105g\u0142e": [[18, "funkcje-ciagle"], [20, "funkcje-ciagle"]], "W\u0142asno\u015bci funkcji ci\u0105g\u0142ych": [[18, "wlasnosci-funkcji-ciaglych"], [20, "wlasnosci-funkcji-ciaglych"]], "Twierdzenie o lokalnym zachowaniu znaku": [[18, null], [20, null]], "Twierdzenie Bezuta": [[18, null], [20, null]], "w\u0142asono\u015b\u0107 Garbouta": [[18, null], [20, null]], "Twierdzenie o osi\u0105ganiu kres\u00f3w": [[18, null], [21, null]], "Twierdzenie o ci\u0105g\u0142o\u015bci funkcji odwrotnej": [[18, null], [21, null]], "Twierdzenie o ci\u0105g\u0142o\u015bci funkcji z\u0142o\u017conej": [[18, null], [21, null]], "Twierdzenie o 4 dzia\u0142aniach dla funkcji ci\u0105g\u0142ych": [[18, null], [21, null]], "Przyk\u0142ady funkcji ci\u0105g\u0142ych": [[18, "przyklady-funkcji-ciaglych"], [21, "przyklady-funkcji-ciaglych"]], "Interpretacja krzywej": [[18, "interpretacja-krzywej"], [22, "interpretacja-krzywej"]], "R\u00f3\u017cniczkowanie": [[18, "rozniczkowanie"], [23, "rozniczkowanie"]], "Definicja pochodnej": [[18, null], [23, null]], "Przyk\u0142ady funkcji pochodnych": [[18, "przyklady-funkcji-pochodnych"], [23, "przyklady-funkcji-pochodnych"]], "Przyk\u0142ady funkcji, kt\u00f3re nie maj\u0105 pochodnych": [[18, "przyklady-funkcji-ktore-nie-maja-pochodnych"], [23, "przyklady-funkcji-ktore-nie-maja-pochodnych"]], "Twierdzenie o ci\u0105g\u0142o\u015bci funkcji r\u00f3\u017cniczkowalnej": [[18, null], [23, null]], "Dzia\u0142ania na pochodnych": [[18, "dzialania-na-pochodnych"], [23, "dzialania-na-pochodnych"]], "Twierdzenie o r\u00f3\u017cniczkowalno\u015bci z\u0142o\u017ce\u0144 funkcji r\u00f3\u017cniczkowalnych": [[18, null], [23, null]], "Pochodne funkcji trygonometrycznych": [[18, "pochodne-funkcji-trygonometrycznych"], [23, "pochodne-funkcji-trygonometrycznych"]], "Pochodna funkcji wyk\u0142adniczej": [[18, "pochodna-funkcji-wykladniczej"], [23, "pochodna-funkcji-wykladniczej"]], "pochodna iloczynu": [[18, null], [24, null]], "pochodna ilorazu": [[18, null], [24, null]], "twierdzenie": [[18, null], [24, null]], "pochodna z\u0142o\u017cenia funkcji": [[18, null], [24, null]], "Pochodna logarytmiczna": [[18, "pochodna-logarytmiczna"], [24, "pochodna-logarytmiczna"]], "Zastosowanie pochodnych": [[18, "zastosowanie-pochodnych"], [25, "zastosowanie-pochodnych"]], "Maksimum lokalne": [[18, null], [25, null]], "Twierdzenie o zerowaniu si\u0119 pochodnych w maksimum lokalnym": [[18, null], [25, null]], "Twierdzenie Lagrange\u2019a o warto\u015bci \u015bredniej": [[18, null], [25, null]], "Twierdzenie Coushy\u2019ego": [[18, null], [25, null]], "Wnioski Tw. Lagrange\u2019a": [[18, "wnioski-tw-lagrangea"], [26, "wnioski-tw-lagrangea"]], "Twierdzenie AGH": [[18, null], [26, null]], "Regu\u0142a de l\u2019Hospitala": [[18, "regula-de-lhospitala"], [18, null], [26, "regula-de-lhospitala"], [26, null]], "Poj\u0119cie R\u00f3\u017cniczki": [[18, "pojecie-rozniczki"], [27, "pojecie-rozniczki"]], "Oznaczenia": [[18, "oznaczenia"], [27, "oznaczenia"]], "Wz\u00f3r Taylora": [[18, "wzor-taylora"], [27, "wzor-taylora"]], "Wz\u00f3r Maclaurina": [[18, null], [27, null]], "Reszta Peano": [[18, "reszta-peano"], [28, "reszta-peano"]], "Ekstrema lokalne": [[18, "ekstrema-lokalne"], [28, "ekstrema-lokalne"]], "Zadania": [[18, "zadania"], [29, "zadania"]], "Wypuk\u0142o\u015b\u0107 funkcji": [[18, "wypuklosc-funkcji"], [29, "wypuklosc-funkcji"]], "Twierdzenie o wypuk\u0142o\u015bci": [[18, null], [29, null]], "Asymptoty": [[18, "asymptoty"], [29, "asymptoty"]], "Sporz\u0105dzanie wykres\u00f3w funkcji": [[18, "sporzadzanie-wykresow-funkcji"], [30, "sporzadzanie-wykresow-funkcji"]], "Rachunek Ca\u0142kowy": [[18, "rachunek-calkowy"], [31, "rachunek-calkowy"]], "definicja ca\u0142ki": [[18, null], [31, null]], "Twierdzenie o sta\u0142ej ca\u0142kowania": [[18, null], [31, null]], "Metody obliczania ca\u0142ek": [[18, "metody-obliczania-calek"], [31, "metody-obliczania-calek"]], "Zgadywanie": [[18, "zgadywanie"], [31, "zgadywanie"]], "Liniowo\u015b\u0107*": [[18, null], [31, null]], "przez cz\u0119\u015bci": [[18, "przez-czesci"], [31, "przez-czesci"]], "Przez podstawienie": [[18, "przez-podstawienie"], [32, "przez-podstawienie"]], "Podstawienie": [[18, null], [32, null]], "Ca\u0142ki funkcji wymiernych": [[18, "calki-funkcji-wymiernych"], [32, "calki-funkcji-wymiernych"]], "Ca\u0142kowanie u\u0142amk\u00f3w prostych": [[18, "calkowanie-ulamkow-prostych"], [33, "calkowanie-ulamkow-prostych"]], "Ca\u0142kowanie Funkcji typu R(cos(x), sin(x))": [[18, "calkowanie-funkcji-typu-r-cos-x-sin-x"], [33, "calkowanie-funkcji-typu-r-cos-x-sin-x"]], "Ca\u0142ki z pierwiastkiem": [[18, "calki-z-pierwiastkiem"], [33, "calki-z-pierwiastkiem"]], "Ca\u0142ka Oznaczona (Rimana)": [[18, "calka-oznaczona-rimana"], [34, "calka-oznaczona-rimana"]], "definicja ca\u0142ki oznaczonej": [[18, null], [34, null]], "W\u0142asno\u015bci ca\u0142ki Rimmana": [[18, "wlasnosci-calki-rimmana"], [34, "wlasnosci-calki-rimmana"]], "Zastosowania ca\u0142ek": [[18, "zastosowania-calek"], [35, "zastosowania-calek"]], "Pole pod wykresem": [[18, "pole-pod-wykresem"], [35, "pole-pod-wykresem"]], "pole elipsy": [[18, null], [35, null]], "Matematyka - \u0107wiczenia": [[36, "matematyka-cwiczenia"], [37, "matematyka-cwiczenia"]], "Wz\u00f3r sterlinga": [[36, null], [37, null]], "Przydatne w\u0142asno\u015bci": [[36, "przydatne-wlasnosci"], [38, "przydatne-wlasnosci"]], "Przyk\u0142adowa tabela przebiegu zmienno\u015bci funkcji:": [[36, "przykladowa-tabela-przebiegu-zmiennosci-funkcji"], [38, "przykladowa-tabela-przebiegu-zmiennosci-funkcji"]], "Triksy": [[36, "triksy"], [38, "triksy"]], "Ca\u0142ki - Istotne wzory / wyprowadzenia": [[36, "calki-istotne-wzory-wyprowadzenia"], [39, "calki-istotne-wzory-wyprowadzenia"]], "Ca\u0142ki Rimmana - tricki / przydatne wzory": [[36, "calki-rimmana-tricki-przydatne-wzory"], [41, "calki-rimmana-tricki-przydatne-wzory"]], "Granice: - Tricki": [[43, "granice-tricki"]], "Symbole Nieoznaczone czyli co z tym robi\u0107?": [[43, "symbole-nieoznaczone-czyli-co-z-tym-robic"]], "0 * \\infty": [[43, "infty"]], "\\infty - \\infty": [[43, "infty-infty"]], "\\frac{\\infty}{\\infty} i \\frac{0}{0}": [[43, "frac-infty-infty-i-frac-0-0"]], "Mechanika - \u0106wiczenia": [[44, "mechanika-cwiczenia"], [46, "mechanika-cwiczenia"]], "Gradient": [[44, null], [46, null]], "Wst\u0119p": [[47, "wstep"]]}, "indexentries": {}}) \ No newline at end of file