Question

Please, help! Need a hint:) lim x-> a: (ln x - ln a) / (x - a)

Answer 1

Recall the definition of the derivative at a point: If $f(x)$ is differentiable at $x=a$, then the derivative at $a$, denoted $f'(a)$, is

$f'(a)=\displaystyle\lim_{x\to a}\frac{f(x)-f(a)}{x-a}$

Here, $f(x)=\ln x$. If you know that $f'(x)=\dfrac1x$, then the limit is simply $\dfrac1a$.