The value of _ x e x-1 x-e is - Vidyadip

MCQ

The value of $\lim _{x \rightarrow e} \frac{\log x-1}{x-e}$ is

A
1
✓
$\frac{1}{ e }$
C
e
D
$0$

✓

Answer

Correct option: B.

$\frac{1}{ e }$

(B)
Applying L-Hospital's rule, we get
$\lim _{x \rightarrow e } \frac{\log x-1}{x- e }=\lim _{x \rightarrow e } \frac{1}{x}=\frac{1}{ e }$

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