Limit: How to take lim[x=>1] (ln(x-1) - x)/(tg PI/2x) ?

[Brunorp]

Can you help me?

 

[stapel]

Can you help me?

Certainly, we can help! But first, we'll need to see what you've tried so far.

When you reply, please clarify what is the meaning of "tg", and what "product" you're indicating with the upper-case product-notation "\(\displaystyle \, \Pi\, \)" (rather than the lower-case geometrical constant "\(\displaystyle \, \pi\, \approx\, 3.14159\)"). Also, if this exercise arose in the homework for a particular section in your textbook, then probably you're expected to use the material from that section. If you could please provide that topic, also. Thank you!

 

[pka]

Can you help me?

For those of us in an Anglo-country it is:
\(\displaystyle \large{\displaystyle\lim _{x \to 1}}\frac{{\log (x - 1) - 1}}{{\tan \left( {\frac{\pi }{{2x}}} \right)}}\)

Use L'Hôpital's rule.