Question

$\underset{x\to e}{lim}\frac{\log x-1}{x-e}$

Answer 1

At $x=e$ , given function will be of form $\frac{0}{0}$. So using L'Hopital's rule:

$\underset{x\to e}{lim}\frac{logx-1}{x-e}=\underset{x\to e}{lim}\frac{\frac{1}{x}-0}{1-0}=\frac{1}{e}$