vault backup: 2023-05-26 08:45:39

!Załączniki/Analiza stałoprądowa 2023-05-09 13.50.06.excalidraw.md

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+---
+
+excalidraw-plugin: parsed
+tags: [excalidraw]
+
+---
+==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
+
+
+# Text Elements
+%%
+# Drawing
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+
+
+```
+%%

.obsidian/core-plugins-migration.json

@@ -25,5 +25,6 @@
   "file-recovery": true,
   "publish": false,
   "sync": false,
-  "canvas": true
+  "canvas": true,
+  "bookmarks": true
 }

.obsidian/core-plugins.json

@@ -13,7 +13,7 @@
   "note-composer",
   "command-palette",
   "editor-status",
-  "starred",
+  "bookmarks",
   "markdown-importer",
   "zk-prefixer",
   "outline",

.obsidian/workspace.json

@@ -8,18 +8,29 @@
         "type": "tabs",
         "children": [
           {
-            "id": "1eb42644e92dcb17",
+            "id": "938ad38d86b932c5",
             "type": "leaf",
             "state": {
               "type": "markdown",
               "state": {
-                "file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
+                "file": "TC/Wykład/7..md",
                 "mode": "source",
                 "source": false
               }
             }
+          },
+          {
+            "id": "455e8a63d7cbabc4",
+            "type": "leaf",
+            "state": {
+              "type": "release-notes",
+              "state": {
+                "currentVersion": "1.2.8"
+              }
+            }
           }
-        ]
+        ],
+        "currentTab": 1
       }
     ],
     "direction": "vertical"
@@ -64,6 +75,14 @@
               "type": "starred",
               "state": {}
             }
+          },
+          {
+            "id": "562379ddd83ebec1",
+            "type": "leaf",
+            "state": {
+              "type": "bookmarks",
+              "state": {}
+            }
           }
         ]
       }
@@ -85,7 +104,7 @@
             "state": {
               "type": "backlink",
               "state": {
-                "file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
+                "file": "TC/Wykład/7..md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -102,7 +121,7 @@
             "state": {
               "type": "outgoing-link",
               "state": {
-                "file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
+                "file": "TC/Wykład/7..md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               }
@@ -125,7 +144,7 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md"
+                "file": "TC/Wykład/7..md"
               }
             }
           },
@@ -206,42 +225,41 @@
       "audio-recorder:Start/stop recording": false,
       "3d-graph:3D Graph": false,
       "juggl:Juggl global graph": false,
-      "obsidian-excalidraw-plugin:Create new drawing": false,
-      "breadcrumbs:Breadcrumbs Visualisation": false
+      "obsidian-excalidraw-plugin:Create new drawing": false
     }
   },
-  "active": "1eb42644e92dcb17",
+  "active": "455e8a63d7cbabc4",
   "lastOpenFiles": [
-    "AMiAL/Ćwiczenia/2 SEM/20230303081617.md",
-    "AMiAL/AMiAL.md",
-    "EiM/EiM.md",
+    "TC/Wykład/8. Przerzutniki.md",
+    "TC/Wykład/7..md",
+    "TC/Wykład/3. ?.md",
+    "TC/Ćwiczenia/aaa.md",
+    "TC/Ćwiczenia/Ćwiczenia.md",
     "TC/TC.md",
+    "EiM/Ćwiczenia/Analiza stałoprądowa.md",
+    "!Załączniki/Analiza stałoprądowa 2023-05-09 13.50.06.excalidraw.md",
+    "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
+    "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 2.md",
+    "AMiAL/!Materiały/calki_1.pdf",
+    "AMiAL/AMiAL.md",
+    "AiSD/AiSD.md",
+    "Elektrotechnika/Ćwiczenia/20230428101941.md",
+    "!Załączniki/20230428101941 2023-04-28 10.39.09.excalidraw.md",
+    "!Załączniki/20230428101941 2023-04-28 10.22.19.excalidraw.md",
+    "AMiAL/Ćwiczenia/2 SEM/20230303081617.md",
+    "EiM/EiM.md",
     "TC/Ćwiczenia/Untitled.md",
     "TC/Wykład/0. Wstęp.md",
     "TC/Wykład/Wykład.md",
     "TC/Ćwiczenia/1. Algebra Boola.md",
-    "TC/Ćwiczenia/aaa.md",
     "TC/Ćwiczenia/2. Realizacja układów na stykach.md",
     "TC/Ćwiczenia/3. Układy iteracyjne.md",
-    "TC/Ćwiczenia/Ćwiczenia.md",
     "TC/Laboratorium/Laboratorium.md",
-    "TC/Wykład/8. Przerzutniki.md",
     "!Załączniki/2. Charakterystyki 2023-04-25 13.49.32.excalidraw.md",
     "EiM/Ćwiczenia/2. Charakterystyki.md",
-    "TIiK/Ćwiczenia/1. Logarytmy.md",
-    "TIiK/Wykład/4..md",
-    "AiSD/Ćwiczenia/2. Ćwiczenia.md",
-    "AiSD/Ćwiczenia/3. Złożoność i czynnik sumacyjny.md",
-    "AiSD/AiSD.md",
-    "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 5.md",
-    "TC/Wykład/6. Układy Sekwencyjne.md",
-    "EiM/Wykłady/1. Wstęp.md",
-    "TIiK/Wykład/2..md",
-    "TIiK/Wykład/3. Łańcuchy markowa.md",
     "!Załączniki/Recording 20230418135018.webm",
     "!Załączniki/Recording 20230418134959.webm",
     "EiM/Ćwiczenia",
-    "AMiAL/!Materiały/calki_1.pdf",
     "AMiAL/!Materiały/w0_intro.pdf",
     "!Załączniki/Excalidraw/Scripts/Downloaded/Normalize Selected Arrows.svg",
     "!Załączniki/Excalidraw/Scripts/Downloaded/Fixed inner distance.svg",

AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md

@@ -56,9 +56,22 @@ $$
 \begin{gather}
 
 \int\frac{x^{2}-x-2}{\sqrt[3]{x^{2}}}dx=\int\frac{x^{2}-x-2}{x^{\frac{2}{3}}}dx=\int \frac{x^{2}}{x^{\frac{2}{3}}}dx-\int \frac{x}{x^{\frac{2}{3}}}dx-\int \frac{2}{x^{\frac{2}{3}}}dx=\\
-=
-
+=\int x^{\frac{4}{3}}dx- \int x^{\frac{1}{3}}dx - \int \frac{2}{x^{\frac{2}{3}}}dx= \frac{3x^{\frac{7}{3}}}{7}- \frac{3x^{\frac{4}{3}}}{4}-2\cdot3x^\frac{1}{3}+C=\\
+=\frac{3x^{2}\sqrt[3]{x}}{7} - \frac{3x\sqrt[3]{x}}{4} -6 \sqrt[3]{x}+C
+ 
 \end{gather}
 $$
+
+## 15.
+$$\begin{gather}
+\int \frac{(x+\sqrt{x})(\sqrt{x}+\sqrt[4]{x})(\sqrt{x}-\sqrt[4]{x})}{x}dx=\int \frac{(x+\sqrt{x})(x - \sqrt{x})}{x}dx= \\
+= \int\frac{x^{2}-x}{x}dx=\int x-1dx = \frac{x^{2}}{2}-x+C
+\end{gather}$$
+## 16.
+$$
+\int\frac{\sqrt{x+2\sqrt{x}+1}}{x}dx=\int \frac{x^{\frac{1}{2}}+1}{x}dx= \int \frac{x^{\frac{1}{2}}}{x}+\int \frac{1}{x}dx=2x^{\frac{1}{2}}+\ln|x|+C
+$$
+## 17.
+$$\int \frac{\sqrt[3]{x}-1}{\sqrt[6]{x}-1}dx=\int\frac{x^{\frac{1}{3}}-1}{x^{\frac{1}{6}}-1}dx=\int\frac{x^{\frac{1}{3}}}{x^{\frac{1}{6}}-1}-\int\frac{1}{x^{\frac{1}{6}}-1}=$$
 ## 18.
 $$\int (4^{x}+2^{-x})dx=\frac{4x}{\ln 4}+ \int (\frac{1}{2})^{x}dx=\frac{4^{x}}{\ln 4}+\frac{(\frac{1}{2})^{x}}{\ln \frac{1}{2}}+c$$

AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 2.md

@@ -0,0 +1,3 @@
+# Obliczyć całki.
+## 1.
+$$\int x \cos x dx=\sin  x +C$$

EiM/Ćwiczenia/Analiza stałoprądowa.md

@@ -0,0 +1,2 @@
+![[Analiza stałoprądowa 2023-05-09 13.50.06.excalidraw]]
+

Elektrotechnika/Ćwiczenia/20230428101941.md

@@ -0,0 +1,10 @@
+| |S|jω|
+|-|-|-|
+|R|R|R|
+|L|Z$_L$=sL|Z$_L$=jωL|
+
+
+![[20230428101941 2023-04-28 10.22.19.excalidraw]]
+
+
+![[20230428101941 2023-04-28 10.39.09.excalidraw]]