In order to find the limit, we need to replace the value of x inside the function for 2.
[tex]\begin{gathered} \lim _{x\to2}\frac{x^3-2x^2+3}{x-1} \\ \text{then,} \\ \lim _{x\to2}\frac{(2)^3-2(2)^2+3}{2-1} \\ \lim _{x\to2}\frac{8-8+3}{1} \\ \lim _{x\to2}3 \\ \lim _{x\to2}\frac{x^3-2x^2+3}{x-1}=3 \end{gathered}[/tex]
