diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 9c6290c..751856a 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -83,26 +83,12 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Trigonometri.md",
+                "file": "Gräsvärde (1).md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "Trigonometri"
-            }
-          },
-          {
-            "id": "fc32ad4cc63e1ba9",
-            "type": "leaf",
-            "state": {
-              "type": "split-diff-view",
-              "state": {
-                "aFile": ".obsidian/workspace.json",
-                "bFile": ".obsidian/workspace.json",
-                "aRef": ""
-              },
-              "icon": "diff",
-              "title": "Diff: workspace.json"
+              "title": "Gräsvärde (1)"
             }
           }
         ],
@@ -266,16 +252,16 @@
       "obsidian-git:Open Git source control": false
     }
   },
-  "active": "e616c86f78b96cf1",
+  "active": "be47d5ede3a9176b",
   "lastOpenFiles": [
     "Trigonometri.md",
-    "Komplexa tal.md",
+    "Grafer.md",
     "Gräsvärde (1).md",
+    "Komplexa tal.md",
     "conflict-files-obsidian-git.md",
     "gv1.png",
     "Funktioner.md",
     "Funktioner Forts.md",
-    "Grafer.md",
     "k2.png",
     "k1.png",
     "f_inverse.png",
diff --git a/Gräsvärde (1).md b/Gräsvärde (1).md
index fbe3ef1..496cf3a 100644
--- a/Gräsvärde (1).md	
+++ b/Gräsvärde (1).md	
@@ -11,11 +11,27 @@
 	- *Derivator, integraler, asymptot etc definieras med hjälp av gränsvärde.*
 	- *Om $a$ int är "problempunkt" stoppar vi in $x=a$ i $f(x)$*
 	- **Def**: *"Problempunkt" t.ex $\lim_{x\to 0}\frac1x$ går inte att direkt lösa på grund av division med $0$*
+	- **Ex**: $$\begin{align}\lim_{x\to5}f(x)=\lim_{x\to5}\frac1x=\frac15\\\lim_{x\to\infty}f(x)=\lim_{x\to\infty}\frac1x=0\\\lim_{x\to0}f(x)=\lim_{x\to0}\frac1x\text{ Existerar inte}\end{align}$$
 - One sided limits
 	- ![[gv1.png]]
+	- **Ex**: $$\begin{align}sgm(x)=\left\{\begin{aligned}1,\;x>0\\0,\;x=0\\-1,\;x<0\end{aligned}\right.\\D_{sgm}=\mathbb{R}\\\lim_{x\to0}sgm(x)\text{ Existerar inte}\\\lim_{x\to0^+}sgm(x)=\lim_{x\to0^+}1=1\\\lim_{x\to0^-}sgm(x)=\lim_{x\to0^-}(-1)=-1\end{align}$$
+	- **Ex**: $$\begin{align}\lim_{x\to a}f(x)\text{ existerar om}\\\lim_{x\to a+}f(x)\&\lim_{x\to a-}f(x)\\\text{ Existerarf och }\lim_{x\to a+}f(x)=\lim_{x\to a-}f(x)\\\\f(x)=\sqrt{x}, D_f=\left[0,\infty\right)\\\lim_{x\to0+}f(x)=\lim_{x\to0+}\sqrt{x}=0\\\\f(x)=\left\{\begin{aligned}x+1,\;x>0\\0,\;x=0\\2x+1,\ x<0\end{aligned}\right.\\D_f=\mathbb{R}\\\lim_{x\to0+}f(x)=\lim_{x\to0+}x+1\\=0+1=1\\\lim_{x\to0-}f(x)=\lim_{x\to0-}2x+1\\=2\times0+1=0\\\lim_{x\to0}f(x)=1\end{align}$$
 - Problem fall
 	- $\left[\frac00\right]$ form: **Ex**: $$\lim_{x\to1}\frac{x^2-3x+2}{x^2-1},\;\lim_{x\to0}\frac{e^x-1}x,\;\lim_{x\to\infty}\frac{\tan{x}}x$$
 	- $\left[\frac\infty\infty\right]$ form: **Ex**: $$\lim_{x\to\infty}\frac{x^2-3x+2}{x^2-1},\;\lim_{x\to\infty}\frac{x^3}{2^x}$$
 	- $\left[0\times\infty\right]$ form: **Ex**: $$\lim_{x\to\infty}x^2\ln\mid{x}\mid$$
 	- $\left[0^0\right]$ form: **Ex**: $$\lim_{x\to0+}x^x$$
-	- $\left[\infty^0\right]$ form **Ex**: $$\lim_{x\to\infty}$$
\ No newline at end of file
+	- $\left[\infty^0\right]$ form **Ex**: $$\lim_{x\to\infty}x^{1/x}$$
+	- $\left[1^\infty\right]$ form: **Ex**: $$\lim_{x\to0}(1+x)^{1/x}$$
+	- $\left[\infty-\infty\right]$ form: $$\lim_{x\to\infty}\left(\sqrt{x^2+5x+1}-\sqrt{x^2+3x-5}\right)$$
+	- **Ex**: $$\begin{align}\lim_{x\to1}\frac{x^2-3x+2}{x^2-1}=\frac{0^2-3\times0+2}{0^2-1}=\frac{1+2}{1-1}=\frac{3}{0}\text{ Fins inget gränsvärde}\\\lim_{x\to1}\frac{x^2-3x+2}{x^2-1}\Longleftrightarrow\lim_{x\to1}\frac{(x-1)(x-2)}{(x-1)(x+1)}=\frac{x-2}{x+1}=\frac{1-2}{1+1}=-\frac12\end{align}$$
+	- **Ex**: $$\lim_{x\to\infty}\frac{x^2-3x+2}{x^2-1}=\lim_{x\to\infty}\frac{1-\frac3x+\frac2{x^2}}{1-\frac1{x^2}}=\frac{1-0+0}{1-0}=1$$
+	- **Ex**: $$$$
+- Räkneregler
+	- *Låt $f$ och $g$ vara funktioner så att $$\lim_{x\to a}f(x)=A,\;\lim_{x\to a}=B,\;\mid{A}\mid<\infty,\;\mid{B}\mid<\infty$$*
+	- $$\lim_{x\to a}\alpha(f(x)+\beta g(x))=\alpha A+\beta B$$
+	- $$\lim_{x\to a}f(x)\times g(x)=A\times B$$
+	- $$\lim_{x\to a}\frac{f(x)}{g(x)}=\frac{A}{B}\text{ om }B\neq0$$
+	- **Theorem**: *Instängningsregel $$\left.\begin{aligned}f(x)\leq g(x)\leq h(x),\;\forall x\\\lim_{x\to a}f(x)=L=\lim_{x\to a}h(x)\end{aligned}\right\}\Rightarrow\lim_{x\to a}g(x)=L$$*
+	- **Theorem**: $$f(X)\leq g(x),\;\forall x\Rightarrow\;\lim_{x\to a}f(x)\leq\lim_{x\to a}g(x)$$
+	- **Theorem**: *Sammansättningsregel $$\left.\begin{aligned}\lim_{x\to a}f(x)=b\\\lim_{x\to b}g(x)=L\end{aligned}\right\}\Leftarrow$$*
\ No newline at end of file