vault backup: 2022-12-02 12:36:09

AMiAL/Wykłady/1 SEM/20221125083233.md

@@ -14,7 +14,7 @@ D_{f}\in(-\infty, 1) \cup (1,2) \cup (2,\infty)\\
 
 \lim_{x\rightarrow1}=
 
-granica pionowa obustronna w 1
+granica\ pionowa\ obustronna\ w\ 1
 \end{gathered}
 $$
 

AMiAL/Ćwiczenia/1 SEM/20221202121227.md

@@ -0,0 +1,18 @@
+$$
+\begin{gathered}
+f(x)=\begin{cases}
+\cfrac{2x^{2}-x-1}{x-1}  &x\ne1\\
+-1 &x = 1
+\end{cases}\\\\\\
+
+D_{f}=\mathbb{R}\\
+\lim_{x\rightarrow1}\frac{2x^{2}-x-1}{x-1}=^{[\frac{0}{0}]}\lim_{x\rightarrow1}\frac{2(x-1)(x+\frac{1}{2})}{x-1}=\lim_{x\rightarrow1}2x+1=3\\
+
+f(1)=-1\\
+\Delta=1+8\\
+\sqrt{\Delta}=3\\
+x_{1}=1\\
+x_{2}= -\frac{1}{2}
+\end{gathered}
+
+$$