vault backup: 2024-09-24 09:39:22

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -12,8 +12,8 @@
   "checkpointList": [
     {
       "path": "/",
-      "date": "2024-09-20",
+      "date": "2024-09-24",
-      "size": 4752037
+      "size": 4982515
     }
   ],
   "activityHistory": [
@@ -1581,20 +1581,44 @@
           "value": 473
         },
         {
-          "date": "2024-09-11",
+          "date": "2024-05-09",
-          "value": 584636
+          "value": 229178
         },
         {
-          "date": "2024-09-16",
+          "date": "2024-05-10",
-          "value": 14
+          "value": 1045
         },
         {
-          "date": "2024-09-17",
+          "date": "2024-05-12",
-          "value": 746
+          "value": 43
         },
         {
-          "date": "2024-09-20",
+          "date": "2024-05-16",
-          "value": 490
+          "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
         }
       ]
     }

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}}}}
+{"^{n+1}$":{"^{n+1}$":{"currentFile":{"count":1,"lastUpdated":1727163394804}}}}

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",

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]]

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
+- Rostoucí $\forall n:a_n<a_{n-1}; a_{n+1}-a_n>0$
-- Nerostoucí
+- Nerostoucí $a_{n+1}-a_n\le0$
-- Klesající
+- Klesající $\forall n:a_n>a_{n-1};a_{n+1}-a_n<0$
-- Neklesající
+- Neklesající $a_{n+1}-a_n\ge0$
 #### Prostota
 - Prostá - neopakují se hodnoty, dá se sestavit inverzní funkce
 #### Parita