From 69f41786ba94f6b8cdea895ce0ec0ebb53767477 Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Tue, 24 Sep 2024 09:39:22 +0200 Subject: [PATCH] vault backup: 2024-09-24 09:39:22 --- .../obsidian-activity-history/data.json | 44 ++++++--- .../various-complements/histories.json | 2 +- notes/.obsidian/workspace.json | 44 ++++----- notes/cjl/cjl.md | 2 +- notes/mat/Posloupnost.md | 89 ++++++++++++++++++- 5 files changed, 143 insertions(+), 38 deletions(-) diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index d5b2806..2ed9d5d 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -12,8 +12,8 @@ "checkpointList": [ { "path": "/", - "date": "2024-09-20", - "size": 4752037 + "date": "2024-09-24", + "size": 4982515 } ], "activityHistory": [ @@ -1581,20 +1581,44 @@ "value": 473 }, { - "date": "2024-09-11", - "value": 584636 + "date": "2024-05-09", + "value": 229178 }, { - "date": "2024-09-16", - "value": 14 + "date": "2024-05-10", + "value": 1045 }, { - "date": "2024-09-17", - "value": 746 + "date": "2024-05-12", + "value": 43 }, { - "date": "2024-09-20", - "value": 490 + "date": "2024-05-16", + "value": 1133 + }, + { + "date": "2024-05-17", + "value": 0 + }, + { + "date": "2024-06-06", + "value": 1517 + }, + { + "date": "2024-06-07", + "value": 581086 + }, + { + "date": "2024-06-08", + "value": 0 + }, + { + "date": "2024-06-09", + "value": 0 + }, + { + "date": "2024-09-24", + "value": 3798 } ] } diff --git a/notes/.obsidian/plugins/various-complements/histories.json b/notes/.obsidian/plugins/various-complements/histories.json index d94ab02..89e9c86 100644 --- a/notes/.obsidian/plugins/various-complements/histories.json +++ b/notes/.obsidian/plugins/various-complements/histories.json @@ -1 +1 @@ -{"Data":{"Data":{"internalLink":{"count":1,"lastUpdated":1726048916652}}},"Termodynamická teplota":{"Termodynamická teplota":{"internalLink":{"count":1,"lastUpdated":1726050276200}}},"Postavy":{"Postavy":{"internalLink":{"count":1,"lastUpdated":1726050359066}}},"prvků":{"prvků":{"currentFile":{"count":1,"lastUpdated":1726557527522}}}} \ No newline at end of file +{"^{n+1}$":{"^{n+1}$":{"currentFile":{"count":1,"lastUpdated":1727163394804}}}} \ No newline at end of file diff --git a/notes/.obsidian/workspace.json b/notes/.obsidian/workspace.json index 5c1713f..be53e10 100644 --- a/notes/.obsidian/workspace.json +++ b/notes/.obsidian/workspace.json @@ -4,11 +4,11 @@ "type": "split", "children": [ { - "id": "6fc77342ea8daf26", + "id": "2c7195dc81f4f010", "type": "tabs", "children": [ { - "id": "61fce6f2d25a77a3", + "id": "30041935835de35c", "type": "leaf", "state": { "type": "markdown", @@ -223,59 +223,59 @@ }, "left-ribbon": { "hiddenItems": { + "juggl:Juggl global graph": false, "switcher:Open quick switcher": false, "graph:Open graph view": false, "canvas:Create new canvas": false, "command-palette:Open command palette": false, "markdown-importer:Open format converter": false, + "obsidian-excalidraw-plugin:Create new drawing": false, + "omnisearch:Omnisearch": false, "table-editor-obsidian:Advanced Tables Toolbar": false, "templater-obsidian:Templater": false, - "obsidian-excalidraw-plugin:Create new drawing": false, - "juggl:Juggl global graph": false, "obsidian-spaced-repetition:Review flashcards": false, - "omnisearch:Omnisearch": false, "obsidian-advanced-slides:Show Slide Preview": false, "breadcrumbs:Breadcrumbs Visualisation": false } }, - "active": "61fce6f2d25a77a3", + "active": "30041935835de35c", "lastOpenFiles": [ - "eko/Marek.md", "mat/Posloupnost.md", - "mat/Funkce/Funkce.md", - "pva/skripta.md", - "pva/vasek.md", - "pva/pva.md", "cjl/Maturita.md", + "mat/Geometrie/Kombinace variace permutace.md", + "data/Kombinace variace permutace 2024-06-07 11.12.16.excalidraw.md", + "data/Pasted Image 20240607123213_059.png", + "data/Pasted Image 20240607120859_000.png", + "data/Pasted Image 20240607113016_141.png", + "data/Kombinace variace permutace 2024-06-07 11.12.16.excalidraw.svg", + "data/Pasted Image 20240607111318_511.png", + "data/Pasted image 20240607110825.png", + "data/Pasted image 20240607110822.png", + "mat/Geometrie/Analytická/Kuželosečky.md", + "mat/Geometrie/Analytická/2 kružnice.md", + "eko/Úvodní hodina.md", + "eko/Marek.md", + "mat/Geometrie/Analytická/Parabola.md", + "mat/mat.md", "mat/Geometrie/Analytická/Příklady.md", "mat/Geometrie/Analytická/kružnice a přímka.md", - "mat/Geometrie/Analytická/Parabola.md", "mat/Funkce/Exponenciální funkce.md", "eko/eko.md", "mat/Geometrie/Analytická/Vektor.md", - "mat/Geometrie/Analytická/Kuželosečky.md", - "mat/mat.md", "eko/Podnikání.md", "eko/Pracovní proces.md", "fyz/elektrika/fotoveci.md", "conflict-files-obsidian-git.md", "export/export.md", "vyp/Cenová politika a swot analýza.md", + "pva/pva.md", "export/Buffer Overflow/Buffer Overflow.md", "data/Příklady 2024-03-15 11.06.56.excalidraw.svg", "data/Příklady 2024-03-15 11.06.56.excalidraw.md", "cjl/literatura/Tropy a figury.md", "mat/Geometrie/Analytická/Hyperbola.md", - "mat/Geometrie/Analytická/Elipsa.md", "data/Parabola 2024-03-22 11.31.41.excalidraw.svg", "data/Parabola 2024-03-21 11.58.33.excalidraw.svg", - "data/Parabola 2024-03-21 11.18.48.excalidraw.svg", - "data/Hyperbola 2024-03-14 11.33.16.excalidraw.svg", - "data/Hyperbola 2024-03-08 12.05.45.excalidraw.svg", - "data/Elipsa 2024-03-01 11.25.47.excalidraw.svg", - "data/Pasted image 20240301122558.png", - "data/Pasted image 20240301120922.png", - "data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg", "export/Buffer Overflow/data", "export/Buffer Overflow/plugin/chalkboard/_style.css", "export/Buffer Overflow/plugin/chalkboard/img", diff --git a/notes/cjl/cjl.md b/notes/cjl/cjl.md index fd6d543..b5095d2 100644 --- a/notes/cjl/cjl.md +++ b/notes/cjl/cjl.md @@ -12,7 +12,7 @@ imagePrefix: 'data/' - [[cjl/jazyky/jazyky|jazyky]] - [[cjl/jména|jména]] - [[cjl/literatura/literatura|literatura]] -- [[Maturita|Maturita]] +- [[cjl/Maturita|Maturita]] - [[cjl/Pedagog a didaktik|Pedagog a didaktik]] - [[cjl/Povinné knihy|Povinné knihy]] - [[cjl/Slohové práce/Slohové práce|Slohové práce]] diff --git a/notes/mat/Posloupnost.md b/notes/mat/Posloupnost.md index 615a5e9..c04006f 100644 --- a/notes/mat/Posloupnost.md +++ b/notes/mat/Posloupnost.md @@ -62,13 +62,94 @@ $-15/2=2a_3$ $a_3=-15/4$ +$a_{n-1}=3n+2a_{n+1}-{a_n}$ +$a_5=1;a_6=7$ + +$a_4=3*5+2*7-1$ +$a_4=15+14-1=28$ + +$a_3=3*4+2*1-28$ +$a_3=12+2-28=-14$ + +$a_2=3*3+2*28+14$ +$a_2=9+56+14=79$ + +$a_5=3*6+2*a_7-7$ +$1=18+2a_7-7=11+2a_7$ +$-2a_7=10$ +$a_7=-5$ + +$a_6=3*7+2*a_8+5$ +$a_6=21+2a_8+5=26+2a_8$ +$7=26+2a_8$ +$2a_8=7-26=-19$ +$a_8=-9.5$ + +--- + +Dokaž že posloupnost je nebo není monotónní; jak? + +$a_n=\frac{n+1}n \rightarrow a_{n+1}=\frac{n+1+1}{n+1}$ + +$a_{n+1}-a_n=\frac{n+2}{n+1}-\frac{n+1}{n}=\frac{(n+2)n}{n(n+1)}-\frac{(n+1)n}{n(n+1)}$ +$\frac{n^2+2n}{n(n+1)}-\frac{(n^2+n)}{n(n+1)}\lt0\forall n \in \mathbb{N}$ +klesajici + +$a_n=\frac{2n+1}{n+2}$ +$a_{n+1}=\frac{2(n+1)+1}{n+1+2}$ + +$\frac{2n+1}{n+2}-\frac{2(n+1)+1}{n+1+2}$ +$\frac{(2n+1)(n+1+2)}{(n+2)(n+1+2)}-\frac{(n+2)(2(n+1)+1)}{(n+2)(n+1+2)}$ + +$\frac{(2n+1)(n+3)-(n+2)(2(n+1)+1)}{(n+2)(n+3)}$ + +$\frac{2n^2+6n+n+3-(2n(n+1)+n+4(n+1)+2)}{(n+2)(n+3)}$ + +$\frac{2n^2+6n+n+3-(2n^2+2n+n+4n+4+2)}{(n+2)(n+3)}$ + +$\frac{2n^2+7n+3-(2n^2+7n+6)}{(n+2)(n+3)}$ + +$\frac{2n^2+7n+3-2n^2-7n-6}{(n+2)(n+3)}$ + +Odečteno ve špatném pořadí! Proto obrácené znaménko +$a_{n+1}-a_n$ + +$\frac{3}{(n+2)(n+3)}>0\forall n\in\mathbb{N}$ + + +--- + +$\{n(-1)^n\}^\infty_1$ + +Přímý důkaz: +$a_n=n(-1)^n$ + +$a_{n+1}=(n+1)(-1)^{n+1}$ + +$(n+1)(-1)^{n+1}-n(-1)^n$ + +$(n+1)(-1)(-1)^n-n(-1)^n$ + +$(-1)^n[-n-1-n]$ + +$\pm$ vlevo +$-$ vpravo + +Sporem: + +$a_1=-1$ +$a_2=2$ +$a_3=-3$ + +Není monotóní - sporem jsme dokázali neplatnost podmínek pro monotónost + ## Funkce ### Vlastnosti #### Monotónost -- Rostoucí -- Nerostoucí -- Klesající -- Neklesající +- Rostoucí $\forall n:a_n0$ +- Nerostoucí $a_{n+1}-a_n\le0$ +- Klesající $\forall n:a_n>a_{n-1};a_{n+1}-a_n<0$ +- Neklesající $a_{n+1}-a_n\ge0$ #### Prostota - Prostá - neopakují se hodnoty, dá se sestavit inverzní funkce #### Parita