Evaluate $\underset{x→1}{\lim}\frac{x^2-x\log x+\log x-1}{x-1}$.

0 1 2 3

2

$\underset{x→1}{\lim}\frac{x^2-x\log x+\log x-1}{x-1}(\frac{→0}{→0})=\underset{x→1}{\lim}\frac{(x-1)(x+1-\log x)}{x-1}=\underset{x→1}{\lim}(x+1-\log x)$ = 1 + 1 - 0 = 2