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Daniel Bulant 2024-12-13 13:07:28 +01:00
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60
notes/.obsidian/plugins/obsidian-activity-history/data.json vendored
View file

@ -12,8 +12,8 @@
"checkpointList": [ "checkpointList": [
{ {
"path": "/", "path": "/",
"date": "2024-11-04", "date": "2024-12-13",
"size": 4790939 "size": 5786283
} }
], ],
"activityHistory": [ "activityHistory": [
@ -1663,6 +1663,62 @@
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},
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},
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},
{
"date": "2024-12-13",
"value": 0
} }
] ]
} }

2
notes/.obsidian/plugins/obsidian-spaced-repetition/data.json vendored
View file

@ -38,7 +38,7 @@
"maxLinkFactor": 1, "maxLinkFactor": 1,
"showDebugMessages": false "showDebugMessages": false
}, },
"buryDate": "2024-11-04", "buryDate": "2024-12-12",
"buryList": [], "buryList": [],
"historyDeck": null "historyDeck": null
} }

2
notes/.obsidian/plugins/various-complements/histories.json vendored
View file

@ -1 +1 @@
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389
notes/.obsidian/workspace.json vendored
View file

@ -4,24 +4,37 @@
"type": "split", "type": "split",
"children": [ "children": [
{ {
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"type": "tabs", "type": "tabs",
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"type": "leaf", "type": "leaf",
"state": { "state": {
"type": "markdown", "type": "markdown",
"state": { "state": {
"file": "mat/Posloupnost.md", "file": "mat/Diff/Limita.md",
"mode": "source", "mode": "source",
"source": false "source": false
}, },
"icon": "lucide-file", "icon": "lucide-file",
"title": "Posloupnost" "title": "Limita"
}
},
{
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"type": "leaf",
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"type": "excalidraw",
"state": {
"file": "data/Limita 2024-12-12 13.00.01.excalidraw.md"
},
"icon": "excalidraw-icon",
"title": "Limita 2024-12-12 13.00.01.excalidraw"
} }
} }
] ],
"currentTab": 1
} }
], ],
"direction": "vertical" "direction": "vertical"
@ -295,22 +308,312 @@
"state": { "state": {
"type": "review-queue-list-view", "type": "review-queue-list-view",
"state": {}, "state": {},
"icon": "SpacedRepIcon", "icon": "lucide-file",
"title": "Notes Review Queue" "title": "Plugin no longer active"
} }
}, },
{ {
"id": "08ad667046dd5c03", "id": "08ad667046dd5c03",
"type": "leaf", "type": "leaf",
"state": { "state": {
"type": "graph-analysis", "type": "empty",
"state": {}, "state": {},
"icon": "GA-ICON", "icon": "lucide-file",
"title": "Graph Analysis" "title": "New tab"
}
},
{
"id": "ee368f3375611dba",
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"icon": "lucide-file",
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}
},
{
"id": "1a89a174584e4483",
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}
},
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}
},
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}
},
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}
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},
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}
},
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}
},
{
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}
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}
},
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"id": "6c80c658aa96c827",
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}
},
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"id": "a510418dbcfeb1c3",
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}
},
{
"id": "03a1baa236460f49",
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"state": {},
"icon": "lucide-file",
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}
},
{
"id": "5fbed1a7f12975e7",
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}
},
{
"id": "6ab9f992311b39e6",
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"state": {
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"state": {},
"icon": "lucide-file",
"title": "Plugin no longer active"
}
},
{
"id": "e0303c78c4aaa5de",
"type": "leaf",
"state": {
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"state": {},
"icon": "lucide-file",
"title": "Plugin no longer active"
}
},
{
"id": "2fa81576e1a6f9e9",
"type": "leaf",
"state": {
"type": "empty",
"state": {},
"icon": "lucide-file",
"title": "New tab"
}
},
{
"id": "c2a1e2cdcf085ed2",
"type": "leaf",
"state": {
"type": "review-queue-list-view",
"state": {},
"icon": "lucide-file",
"title": "Plugin no longer active"
}
},
{
"id": "68b21ad214b16669",
"type": "leaf",
"state": {
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"state": {},
"icon": "lucide-file",
"title": "New tab"
}
},
{
"id": "1e15f60573a9851b",
"type": "leaf",
"state": {
"type": "review-queue-list-view",
"state": {},
"icon": "SpacedRepIcon",
"title": "Notes Review Queue"
} }
} }
], ],
"currentTab": 19 "currentTab": 48
} }
], ],
"direction": "horizontal", "direction": "horizontal",
@ -333,44 +636,47 @@
"obsidian-advanced-slides:Show Slide Preview": false "obsidian-advanced-slides:Show Slide Preview": false
} }
}, },
"active": "08ad667046dd5c03", "active": "4d0a45f845651006",
"lastOpenFiles": [ "lastOpenFiles": [
"data/Pasted Image 20241212130016_247.png",
"mat/Diff/Limita.md",
"data/Limita 2024-12-12 13.00.01.excalidraw.md",
"mat/Diff/Diferencialni pocet.md",
"eko/marek2.md",
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"data/Limita 2024-12-05 13.56.12.excalidraw.svg",
"data/Pasted image 20241203091625.png",
"mat/Diff/deleni.md",
"mat/Diff/Diff.md",
"cjl/Slohové postupy.md",
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"cjl/Slohové práce/Slohové práce.md",
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"data/Pasted Image 20241112150503_253.png",
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"Excalidraw/Drawing 2024-11-12 15.04.32.excalidraw.md",
"mat/maturita/maturita.md",
"mat/maturita",
"data/Pasted image 20241024140155.png", "data/Pasted image 20241024140155.png",
"data/Pasted image 20241024132348.png", "data/Pasted image 20241024132348.png",
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"mat/Posloupnost.md",
"data/Pasted image 20241022073250.png",
"data/Pasted image 20241022070908.png",
"eko/Hospodarsky proces.md", "eko/Hospodarsky proces.md",
"eko/Marek.md", "eko/Marek.md",
"eko/Podnikání.md", "eko/Podnikání.md",
"eko/Majetek.md", "eko/Majetek.md",
"eko/Úvodní hodina.md", "eko/Úvodní hodina.md",
"mat/mat.md", "mat/mat.md",
"cjl/ceska poezie mezivalecna.md",
"eko/eko.md",
"eko/Výrobní faktory.md",
"data/Posloupnost 2024-09-26 13.01.57.excalidraw.md",
"cjl/Básně.md",
"conflict-files-obsidian-git.md",
"mat/Funkce/Funkce.md",
"pva/skripta.md",
"pva/vasek.md",
"pva/pva.md",
"cjl/Maturita.md",
"mat/Geometrie/Analytická/Příklady.md",
"mat/Geometrie/Analytická/kružnice a přímka.md",
"mat/Geometrie/Analytická/Parabola.md",
"mat/Funkce/Exponenciální funkce.md",
"mat/Geometrie/Analytická/Vektor.md",
"mat/Geometrie/Analytická/Kuželosečky.md",
"data/Příklady 2024-03-15 11.06.56.excalidraw.svg",
"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",
"export/Buffer Overflow/data", "export/Buffer Overflow/data",
"export/Buffer Overflow/plugin/chalkboard/_style.css", "export/Buffer Overflow/plugin/chalkboard/_style.css",
"export/Buffer Overflow/plugin/chalkboard/img", "export/Buffer Overflow/plugin/chalkboard/img",
@ -378,9 +684,6 @@
"export/Buffer Overflow/plugin/chalkboard/plugin.js", "export/Buffer Overflow/plugin/chalkboard/plugin.js",
"export/Buffer Overflow/plugin/chalkboard/plugin (copy).js", "export/Buffer Overflow/plugin/chalkboard/plugin (copy).js",
"export/Buffer Overflow/plugin/chalkboard", "export/Buffer Overflow/plugin/chalkboard",
"export/Buffer Overflow/plugin/chart/plugin.js",
"export/Buffer Overflow/plugin/chart/chart.min.js",
"export/Buffer Overflow/plugin/chart",
"Untitled.canvas" "Untitled.canvas"
] ]
} }

15
notes/Excalidraw/Drawing 2024-11-12 15.04.32.excalidraw.md Normal file
View file

@ -0,0 +1,15 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
%%
# Drawing
```json
{"type":"excalidraw","version":2,"source":"https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/1.9.27","elements":[],"appState":{"gridSize":null,"viewBackgroundColor":"#ffffff"}}
```
%%

2
notes/Excalidraw/Excalidraw.md
View file

@ -9,7 +9,9 @@ imagePrefix: 'data/'
- [[Excalidraw/Drawing 2023-12-14 15.41.10.excalidraw|Drawing 2023-12-14 15.41.10.excalidraw]] - [[Excalidraw/Drawing 2023-12-14 15.41.10.excalidraw|Drawing 2023-12-14 15.41.10.excalidraw]]
- [[Excalidraw/Drawing 2023-12-14 19.19.50.excalidraw.svg|Drawing 2023-12-14 19.19.50.excalidraw.svg]] - [[Excalidraw/Drawing 2023-12-14 19.19.50.excalidraw.svg|Drawing 2023-12-14 19.19.50.excalidraw.svg]]
- [[Excalidraw/Drawing 2023-12-14 19.19.50.excalidraw|Drawing 2023-12-14 19.19.50.excalidraw]] - [[Excalidraw/Drawing 2023-12-14 19.19.50.excalidraw|Drawing 2023-12-14 19.19.50.excalidraw]]
- [[Excalidraw/Drawing 2024-01-21 20.54.05.excalidraw.svg|Drawing 2024-01-21 20.54.05.excalidraw.svg]]
- [[Excalidraw/Drawing 2024-01-21 20.54.05.excalidraw|Drawing 2024-01-21 20.54.05.excalidraw]] - [[Excalidraw/Drawing 2024-01-21 20.54.05.excalidraw|Drawing 2024-01-21 20.54.05.excalidraw]]
- [[Excalidraw/Drawing 2024-11-12 15.04.32.excalidraw|Drawing 2024-11-12 15.04.32.excalidraw]]
- [[Excalidraw/Rezistor-example1.excalidraw.svg|Rezistor-example1.excalidraw.svg]] - [[Excalidraw/Rezistor-example1.excalidraw.svg|Rezistor-example1.excalidraw.svg]]
- [[Excalidraw/Rezistor-example1.excalidraw|Rezistor-example1.excalidraw]] - [[Excalidraw/Rezistor-example1.excalidraw|Rezistor-example1.excalidraw]]
- [[Excalidraw/tek-preruseni-jedna.excalidraw|tek-preruseni-jedna.excalidraw]] - [[Excalidraw/tek-preruseni-jedna.excalidraw|tek-preruseni-jedna.excalidraw]]

24
notes/cjl/Slohové postupy.md Normal file
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@ -0,0 +1,24 @@
# Slohové postupy
## Funkční styly
Prostě sdělovací
- plakát, reklama
- pozvánka
- blog, deníček
Odborný
- výklad
Administrativní
Informační
- potvrzení, stvrzenka
- publicistika
Publicistický
- reportáž - musí být na místě, objektivní
- recenze - hodnocení uměleckého díla
- fejeton - humorná kritika, podčarník, próza
Řečnický
- projev, kázání, přednáška, výklad
Umělecký
- epigram humorná báseň, poezi
- líčení umělecký (citově zabarvený) popis
- popis

1
notes/cjl/cjl.md
View file

@ -17,6 +17,7 @@ imagePrefix: 'data/'
- [[cjl/Maturita|Maturita]] - [[cjl/Maturita|Maturita]]
- [[cjl/Pedagog a didaktik|Pedagog a didaktik]] - [[cjl/Pedagog a didaktik|Pedagog a didaktik]]
- [[cjl/Povinné knihy|Povinné knihy]] - [[cjl/Povinné knihy|Povinné knihy]]
- [[cjl/Slohové postupy|Slohové postupy]]
- [[cjl/Slohové práce/Slohové práce|Slohové práce]] - [[cjl/Slohové práce/Slohové práce|Slohové práce]]
- [[cjl/Témata projevu|Témata projevu]] - [[cjl/Témata projevu|Témata projevu]]
- [[cjl/testy/testy|testy]] - [[cjl/testy/testy|testy]]

744
notes/data/Limita 2024-12-05 13.56.12.excalidraw.md Normal file
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@ -0,0 +1,744 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
-3 ^5uASF2js
2 ^t7RoCotd
%%
# Drawing
```json
{
"type": "excalidraw",
"version": 2,
"source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/1.9.27",
"elements": [
{
"id": "sT37U6KhsgXOcOh2Ih0Fa",
"type": "line",
"x": -482.6448059082031,
"y": 27.207801818847656,
"width": 627.1422729492188,
"height": 9.128662109375,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": {
"type": 2
},
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notes/data/data.md
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@ -86,6 +86,9 @@ imagePrefix: 'data/'
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- [[data/Kužolosečky 2024-02-15 11.00.14.excalidraw|Kužolosečky 2024-02-15 11.00.14.excalidraw]] - [[data/Kužolosečky 2024-02-15 11.00.14.excalidraw|Kužolosečky 2024-02-15 11.00.14.excalidraw]]
- [[data/Kužolosečky 2024-02-15 11.01.27.excalidraw|Kužolosečky 2024-02-15 11.01.27.excalidraw]] - [[data/Kužolosečky 2024-02-15 11.01.27.excalidraw|Kužolosečky 2024-02-15 11.01.27.excalidraw]]
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2
notes/eko/eko.md
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@ -3,10 +3,12 @@
- [[eko/Hospodarsky proces|Hospodarsky proces]] - [[eko/Hospodarsky proces|Hospodarsky proces]]
- [[eko/Majetek|Majetek]] - [[eko/Majetek|Majetek]]
- [[eko/Marek|Marek]] - [[eko/Marek|Marek]]
- [[eko/marek2|marek2]]
- [[eko/Podnikání|Podnikání]] - [[eko/Podnikání|Podnikání]]
- [[eko/Pracovní proces|Pracovní proces]] - [[eko/Pracovní proces|Pracovní proces]]
- [[eko/Trh|Trh]] - [[eko/Trh|Trh]]
- [[eko/Úvodní hodina|Úvodní hodina]] - [[eko/Úvodní hodina|Úvodní hodina]]
- [[eko/vypocty|vypocty]]
- [[eko/Výrobní faktory|Výrobní faktory]] - [[eko/Výrobní faktory|Výrobní faktory]]
- [[eko/Vztahy stat - obyvatelstvo|Vztahy stat - obyvatelstvo]] - [[eko/Vztahy stat - obyvatelstvo|Vztahy stat - obyvatelstvo]]
- [[eko/Vztahy stat - podnik|Vztahy stat - podnik]] - [[eko/Vztahy stat - podnik|Vztahy stat - podnik]]

32
notes/eko/marek2.md
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@ -135,6 +135,13 @@ SZP = 3768 * 0.11
Daň = 3768 * 0.15 - 2570 (základní sleva na dani) - 1267 (sleva na první dítě) Daň = 3768 * 0.15 - 2570 (základní sleva na dani) - 1267 (sleva na první dítě)
ČM = 29129 ČM = 29129
$200*8.5$
$400*17$
$600*25$
k teto mzde byla premie $18$%
Test 12/12 Test 12/12
> 5\. 12. 2023 (9. hodina) SZP > 5\. 12. 2023 (9. hodina) SZP
## Sociální a Zdravotní pojišťění ## Sociální a Zdravotní pojišťění
@ -152,7 +159,30 @@ SZB = 11% z HM
### Nemocenské pojištění ### Nemocenské pojištění
- DNP (Dávky nemocenského pojištění) - DNP (Dávky nemocenského pojištění)
> 19\. 12. 2023 (11. hodina) Oprava písemné práce > 19\. 12. 2023 (11. hodina) Oprava písemné práce\
## Rocni zuctovani dane z pr. f. o.
Zaměstnanci je měsíčně strhávána daň z příjmu jako zálohová daň.
HM=40000
RHM=480000
R. daň = 41160
V ročním počítání daně může zaměstnanec použít odpočitatelné položky z daně základu,
např. penzijní připojištění nebo životní pojištění, úroky z hypotéky
Příklad:
penz. přip. 24000
život. poj. 24000
odpočitatelné položky: 48000
d. základ: RHM-odpoč.pol.=480000-48000=432000
nová daň$=432000*0.15-12*2570=33960$
Zaplatil-li již 41160, jedná se o přeplatek a stát vrátí peníze (na účet, do budoucna jako kredit)
## Inf. systém podniky ## Inf. systém podniky
- informace = údaj s **významem** - informace = údaj s **významem**
1. čas (minulé / budoucí) 1. čas (minulé / budoucí)

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# vypocty
140kc/h
12dni v mesici
8h ranni smena
zbytek mesice, 9 pracovnich dnu
odpoledni smena
7.5h
128kc/h
+2% priplatek
k zakladni mzde
25% premie
$27816$
11.6%
15% dan - 2570 zakladni sleva
$22986.9$

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# Diferencialni pocet
$$f(x)=-x^2-2x+1$$
$$D_f=\mathbb{R}$$
$$H_f=(-\infty;2>$$
je omezená shora
není omezená
na $(\infty;-1>$ je rostouci
na $<-1;\infty)$ je klesajici
---
$$f(x)=\sqrt{\frac{x+4}{1-x}}$$
nesmí být nula dole
$1-x=0$ => $x=1$
nesmí být záporné
$\frac{x+4}{1-x}>0$
$x+4>0\cap1-x<0$
$x+4<0\cap1-x>0$
$x<1$
---
$y=\cos(2x-\pi)+1$
---
![[Pasted image 20241203091625.png]]
| | A | B | C | D | E |
| ------------- | --- | --- | --- | --- | --- |
| omezená shora | | | x | | x |
| prostá | x | x | | x | |
| monotónní | x | x | | x | |
| spojitá | x | x | | x | x |
inverzni funkce k
$f:y=\frac13x-\frac25;x\in(-6;3)$
$D_{f^{-1}}=H_f$

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# Diff
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[mat/Diff/deleni|deleni]]
- [[mat/Diff/Diferencialni pocet|Diferencialni pocet]]
- [[mat/Diff/Limita|Limita]]
%% Zoottelkeeper: End of the autogenerated index file list %%

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# Limita
$$\lim_{x\rightarrow\infty}\frac1x=0$$
$$\lim_{x\rightarrow0}\frac{\sin x}x=1$$
## Spojité funkce
když $$f(a)=\lim_{x\rightarrow a}(x)$$funkce je spojitá
$$\lim_{x\rightarrow2}(x^2-3)=1$$
![[Limita 2024-12-05 13.56.12.excalidraw]]
$x^2=4$, dosadí se
$$\lim_{x\rightarrow2}\frac{3x+4}{x^2+1}=\frac{10}5=2$$
$$\lim_{x\rightarrow\frac\pi6}\sin x=\frac12$$
## Nespojité funkce
$$\lim_{x\rightarrow0}=\frac{3x^2-x}x$$
nelze dosadit, funkce je v bodě nespojitá
Jedna možnost, rozdělit limity (upravou se zbavit /x)
$$\lim_{x\rightarrow0}(\frac{3x^2}x-\frac{x}x)=\lim_{x\rightarrow0}(3x-1)=-1$$
$$\lim_{x\rightarrow-1}\frac{x^2+4x+30}{x^3+1}=\lim_{x\rightarrow-1}\frac{(x+1)(x+3)}{(x+1)(x^2-x+1)}=\lim_{x\rightarrow-1}\frac{x+3}{x^2-x+1}=\frac23$$
---
$$\lim_{x\rightarrow7}\frac{2-\sqrt{x-3}}{(x^2-49)}=\lim_{x\rightarrow7}\frac{2-\sqrt{x-3}}{(x+7)(x-7)}$$
$$\lim_{x\rightarrow7}\frac{(2-\sqrt{x-3})(2+\sqrt{x-3})}{(x-7)(x+7)(x+\sqrt{x-3})}$$
$$\lim_{x\rightarrow7}\frac{4-(x-3)}{(x-7)(x+7)(x+\sqrt{x-3})}=\lim_{x\rightarrow7}\frac{-(x-7)}{(x-7)(x+7)(x+\sqrt{x-3})}$$
$$\lim_{x\rightarrow7}\frac{-1}{(x+7)(x+\sqrt{x-3})}$$
$$\frac{-1}{14*(7+2)}=\frac{-1}{14*9}$$
---
$$\lim_{x\rightarrow0}\frac{1-\cos2x}{x^2}$$
$\cos2x=\cos^2x-\sin^2x$
$\cos^2y=\sin^2y=1$
$$\lim_{x\rightarrow0}\frac{1-\cos^2x+\sin^2x}{x^2}$$
$$\lim_{x\rightarrow0}\frac{2*\sin^2x}{x^2}$$
$$\lim_{x\rightarrow0}\frac{2*\sin x*\sin x}{x*x}$$
$2$
---
$\lim_{x\rightarrow+\infty}(4x^3-x^2+x+2)=$
pro $\infty$ a $-\infty$
$\lim_{x\rightarrow\infty}x^2(4x-1)+x+2=$
pro $\infty\rightarrow\infty(\infty-1)+\infty+2=\infty$
pro $-\infty\rightarrow\infty(-\infty)-\infty+2=-\infty$
---
$$\lim_{x\rightarrow\infty}(-4x^3-x^2+x+2)$$
$$\lim_{x\rightarrow\infty}x^3(-4-\frac1x+\frac1{x^2}+\frac2{x^3})$$
$$=-\infty$$
$\frac1x$ a dalsi se blizi nule a “zmizi”
---
$$\lim_{x\rightarrow\infty}\frac{2x^3-x^2+5}{x^2+x-2}$$
----
$$\lim_{x\rightarrow\infty}\frac{\sqrt x-6x}{3x+1}$$
$$\lim_{x\rightarrow\infty}\frac{\sqrt x-6x}{3x+1}\frac{\sqrt x+6x}{\sqrt x+6x}=\lim_{x\rightarrow\infty}\frac{x-36x^2}{3x\sqrt x+18x^2+\sqrt x+6x}$$
$$\lim_{x\rightarrow\infty}\frac{(\frac1x-36)x^2}{x^2(\frac3{\sqrt x}+18+\frac1{x\sqrt x}+\frac6x)}$$
---
$$\lim_{x\rightarrow-4}\frac{x^2-16}{x+4}$$
$$\lim_{x\rightarrow-4}\frac{(x+4)(x-4)}{x+4}$$
$$\lim_{x\rightarrow-4}x-4=-8$$
---
![[Limita 2024-12-12 13.00.01.excalidraw]]

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# deleni
$$(3x^2-5x+1):(2x+1)=\frac32x$$
$-(3x^2-\frac32x)$
$0-\frac{13}2x+1$
$$(3x^2-5x+1):(2x+1)=\frac32x-\frac{13}4$$
$0-\frac{13}2x+1$
$-(-\frac{13}2x-\frac{13}4)$
$0+\frac{17}4$
Seřadíme to podle mocniny
Pak bereme postupně první člen a vydělíme ho celým druhým
Roznásobíme pak prvním mezivýsledkem (vpravo 32x) dělitele, a to odečítáme od zadání
Po odečtení znova dělíme první člen tím vpravo
$\frac{17}4$ je zbytek, doplníme do výsledku jako zlomek:
$$(3x^2-5x+1):(2x+1)=\frac32x-\frac{13}4+\frac{\frac{17}4}{2x+1}$$

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# Limity
$$a_n=\frac{3n+1}n$$
$$\lim_{n\rightarrow\infty}\frac{3n+1}n=\lim_{n\rightarrow\infty}(\frac{3n}n+\frac1n)=3+0=3$$
$$a_n=\frac{2n}5$$
$$\lim_{n\rightarrow\infty}\frac{2n}5=\infty$$
$$\lim_{n\rightarrow\infty}\frac{2n^2+3}{4n}=\lim_{n\rightarrow\infty}(\frac{2nn}{4n}+\frac3{4n})=\lim_{n\rightarrow\infty}(\frac{n}2+\frac{3}{4n})=\infty+0$$
$$\lim_{n\rightarrow\infty}\frac{2-3n}{5n+1}=\lim_{n\rightarrow\infty}(\frac{2}{5n+1}-\frac{3n}{5n+1})=-\frac35$$
$$\lim_{n\rightarrow\infty}\frac{3n^2-2n+1}{-5n^2+n-2}=\lim_{n\rightarrow\infty}(\frac{1}{-5n^2+n-2}+\frac{3n^2-2n}{-5n^2+n-2})=\lim_{n\rightarrow\infty}\frac{3n-2}{-5n+1-\frac2n}=-\frac35$$
$$\lim_{n\rightarrow\infty}-2n^2-3=\infty$$
$$\lim_{n\rightarrow\infty}\frac{2n-3}{1-3n^2}=0$$
$$\lim_{n\rightarrow\infty}\sin n$$ není
$$\lim_{n\rightarrow\infty}\sin(n\pi)=0$$
$$\lim_{n\rightarrow\infty}\log_3n=\infty$$ $$\lim_{n\rightarrow\infty}=-\infty$$
$$\lim_{n\rightarrow\infty}\frac{n-3n^4}{2n^4}=-\frac32$$
$$\lim_{n\rightarrow\infty}(-1)^n3$$ nemá
$$\lim_{n\rightarrow\infty}(-1)^n+2n=\infty$$
$$\lim_{n\rightarrow\infty}(-1)^n\frac3n=0$$

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# Nekonečná geometrická řada
$a_i$ .. členy GP
$$\exists \sum^\infty_{i=1}a_i\Leftrightarrow GP\space je\space konvergentní$$
GP je konv $\Leftrightarrow |q|\lt1$
$$\sum_{i=1}^\infty a_i=\frac{a_1}{1-q}$$
$$\sum_{i=1}^\infty 10^{-n}=\frac{10^{-1}}{1-0.1}=\frac{10^-1}{9*10^{-1}}=\frac19$$
$q=\frac{a_{n+1}}{a_n}$
$q=\frac{10^{-(n+1)}}{10^{-n}}$
$q=0.1$
---
$0.\overline4$
$4*10^{2-n}$
$$\sum^\infty_{n=1}4*10^{2-n}$$
$$q=\frac{4*10^{3-n}}{4*10^{2-n}}=\frac{10^{3-n}}{10^{2-n}}$$
---
Do čtverce ABCD s délkou strany 1 je vepsán nový čtverec, jehož vrcholy leží ve středech stran většího čtverce, atd. Vypočtěte součet obvodů a soušet obsahů všech takových čtverců.
$4+4*\sqrt{0.5}+4*\sqrt{0.5}^2...$
Obvod:
$$\sum^\infty_{n=1}4*\sqrt{0.5}^{n-1}=\frac{4}{1-\sqrt{0.5}}$$
$q=\frac{4*\sqrt2^{n-1+1}}{4*\sqrt2^{n-1}}$
$q=\frac{4\sqrt2^n}{4\sqrt2^{n-1}}$
$q=\frac{\sqrt2^n}{\sqrt2^{n-1}}=\frac{\sqrt2^n}{\sqrt2^n\frac1{\sqrt2}}$
(preklep z 2)
$q=\sqrt{0.5}$
$a_1=4$
Obsah:
$$\sum^\infty_{n=1}(\sqrt{0.5}^{n-1})^2=\frac{1}{1-0.5}=\frac12$$
$a_n=\sqrt{0.5}^{2(n-1)}$
$a_1=1$
$q=\frac{\sqrt2^{2(n-1+1)}}{\sqrt2^{2(n-1)}}$
$q=\frac{\sqrt2^{2(n-1)}*\sqrt{0.5}^2}{\sqrt2^{2(n-1)}}$
$q=\sqrt{0.5}^2=0.5$

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@ -566,10 +566,45 @@ $V=a_1*a_1q*a_1q^2=a_1^3q^3=64$
$a_1+a_2+a_3=84cm$ $a_1+a_2+a_3=84cm$
$a_1+a_1q+a_1q^2=84$ $a_1+a_1q+a_1q^2=84$
$a_1(1+q+q^2)=84$ $a_1(1+q+q^2)=84$`
$4S_3=4a_1\frac{q^3-1}{q-1}=84$ $4S_3=4a_1\frac{q^3-1}{q-1}=84$
--- ---
$$\lim_{n\rightarrow\infty}a_n=a\Leftrightarrow$$
$$\forall\varepsilon>0\exists n_0\in\mathbb{N}:\forall n\ge n_0$$
platí: $a_n\in(a-\varepsilon;a+\varepsilon)$
→ posloupnost je konvergentní
$$\lim_{n\rightarrow\infty}\frac1{n}=0$$
$$\lim_{n\rightarrow\infty}3=3$$
$$lim_{n\rightarrow\infty}\frac1{2n+3}=0$$
$n$ jde do nekonečna, a proto to bude v podstatě $\frac1\infty$
$\infty+\infty=\infty$
$-\infty-\infty=-\infty$
$\pm k*(\pm\infty)=$ pravidlo součinu
$\infty*\infty=\infty$
$-\infty*(-\infty)=\infty$
$\infty*(-\infty)=-\infty$
Není definováno:
$0*\infty$
$\infty-\infty$
$\frac\infty\infty$
$\infty^0$
$1^\infty$
$0^0$
$\frac00$
Vypočti limity:
$$\lim_{n\rightarrow\infty}\frac{n+1}n=\lim_{n\rightarrow\infty}(1+\frac1n)=1$$
$1 \rightarrow 1;\frac1n\rightarrow0$
$$\lim_{n\rightarrow\infty}\frac{1+n}{2n}=\lim_{n\rightarrow\infty}(\frac1{2n}+\frac{n}{2n})=0.5$$
$$\lim_{n\rightarrow\infty}\frac{(-1)^n+n}n$$

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%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[mat/Posloupnosti/Limity|Limity]]
- [[mat/Posloupnosti/Nekonečná geometrická řada|Nekonečná geometrická řada]]
- [[mat/Posloupnosti/Posloupnost|Posloupnost]]
%% Zoottelkeeper: End of the autogenerated index file list %%

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@ -10,6 +10,7 @@ imagePrefix: 'data/'
- [[mat/Absolutní hodnota|Absolutní hodnota]] - [[mat/Absolutní hodnota|Absolutní hodnota]]
- [[mat/Číselné obory|Číselné obory]] - [[mat/Číselné obory|Číselné obory]]
- [[mat/Číselné soustavy|Číselné soustavy]] - [[mat/Číselné soustavy|Číselné soustavy]]
- [[mat/Diff/Diff|Diff]]
- [[mat/Druhá odmocnina|Druhá odmocnina]] - [[mat/Druhá odmocnina|Druhá odmocnina]]
- [[mat/Ekvigonala|Ekvigonala]] - [[mat/Ekvigonala|Ekvigonala]]
- [[mat/Funkce/Funkce|Funkce]] - [[mat/Funkce/Funkce|Funkce]]
@ -18,12 +19,13 @@ imagePrefix: 'data/'
- [[mat/Lomené výrazy/Lomené výrazy|Lomené výrazy]] - [[mat/Lomené výrazy/Lomené výrazy|Lomené výrazy]]
- [[mat/Lomené výrazy|Lomené výrazy]] - [[mat/Lomené výrazy|Lomené výrazy]]
- [[mat/Matematika|Matematika]] - [[mat/Matematika|Matematika]]
- [[mat/maturita/maturita|maturita]]
- [[mat/Mnohočlen|Mnohočlen]] - [[mat/Mnohočlen|Mnohočlen]]
- [[mat/Množiny|Množiny]] - [[mat/Množiny|Množiny]]
- [[mat/Mocniny|Mocniny]] - [[mat/Mocniny|Mocniny]]
- [[mat/Násobek a dělitel|Násobek a dělitel]] - [[mat/Násobek a dělitel|Násobek a dělitel]]
- [[mat/Nerovnice|Nerovnice]] - [[mat/Nerovnice|Nerovnice]]
- [[mat/Posloupnost|Posloupnost]] - [[mat/Posloupnosti/Posloupnosti|Posloupnosti]]
- [[mat/Příklady 1|Příklady 1]] - [[mat/Příklady 1|Příklady 1]]
- [[mat/Příklady 2|Příklady 2]] - [[mat/Příklady 2|Příklady 2]]
- [[mat/README|README]] - [[mat/README|README]]

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# Planimetrie a stereometrie
![[Planimetrie a stereometrie 2024-11-12 15.04.48.excalidraw]]

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%% Zoottelkeeper: Beginning of the autogenerated index file list %%
- [[mat/maturita/Planimetrie a stereometrie|Planimetrie a stereometrie]]
%% Zoottelkeeper: End of the autogenerated index file list %%