I would like to calculate limit: $ \lim_{n \to \infty}{n\cdot \ln({1-\arctan{\frac{3}{n}}})} $ I would like to calculate the following limit:
$$ \lim_{n \to \infty}{n\cdot \ln({1-\arctan{\frac{3}{n}}})} $$
We had this in an exam and I wasn't sure how to go about it. I guess I could try to play with it and use L'Hopitals, is there any easier way to go about it?
Any help would be greatly appreciated.

Substitute the limit $n = {1\over x}$ and use L'Hospital's rule:
$$ \lim_{n \to \infty}{n\cdot \ln({1-\arctan{\frac{3}{n}}})} =\lim_{x \to 0}{{\ln({1-\arctan{3x}}})\over x}   =\lim_{x \to 0} {-3\cos^2(\arctan(3x))\over{{1-\arctan{3x}}}} = -3$$
