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)(f(x)-f(a))/(x-a)`

Here,
`f(x)=\ln x`. If you know that
`f'(x)=\frac1x`, then the limit is simply
`\frac1a`.