Most Captchas aim to separate humans from spambots, but a few creative Captchas floating on the Web probably aim to separate the super-humans from the mere mortals. Tongue-in-cheek aside, I'd definitely like to see more topological Captchas like the one above.
Geek Technica has a neat list of 10 such Captcas that have gone a bit too far in proving that you're human: http://geektechnica.com/2010/06/10-craziest-captchas-out-there/
:D
I think it might be E. But I'm not sure.
Took me more than 29 seconds though.
ln(2) for the math limit one, because arctan(x) goes to 0 while sin(1/x) can only bounce back and forth widely between -1 and 1. However, the sqrt won't like the parts of the function when sin(1/x) is negative, but if sqrt(-1) is allowed and we make this a complex function you would still get to ln(2) eventually. Probably should expand the functions into Taylor series and then do the limit (maybe use L'Hopital's rule also) to get a more rigorous result. Coincidentally, It also goes to ln(2) when x goes to infinity, this time because sin(1/x) goes to zero.
Braille:
?k_ynn__wa_s__here