limits

Question

what is the value of
$\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$

Comments

Use L'hospital and should be 1

Answer 1

$\textstyle \lim_{x \to 2}\frac{(x-2)}{log(x-1)}$                      $\frac{0}{0} form$                      

Apply L Hospital's rule

$\textstyle \lim_{x \to 2}\frac{(1)}{\frac{1}{x-1} \times 1}$

$\textstyle \lim_{x \to 2}(x-1)$

$2-1$

$=1$

Answer 2

1 is the answer