vault backup: 2023-10-03 08:10:20

AMiAL/ICT/Ćwiczenia/1 SEM/20221202121227.md

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