Question

Evaluate : ${lim}_{y\to e}\left(\frac{\ell n\left(y\right)-1}{y-e}\right)$

Answer 1

We have,

${lim}_{y\to e}\frac{\ln y-1}{y-e}$

Apply L-hospital rule,

$={lim}_{y\to e}\frac{\frac{1}{y}-0}{1-0}$

$={lim}_{y\to e}\frac{1}{y}$

$=\frac{1}{e}$

Hence, this is the answer.