Polsl-Notes/AMiAL/ICT/Ćwiczenia/1 SEM/20221202121227.md

\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}