Question

Limit problem solved with knots! Continued from here: http://openstudy.com/study#/updates/543ddbd9e4b0ca823c8e0673

Answer 1

\[\LARGE \lim_{x \rightarrow \infty} \frac{x}{1+xy}\]
Let's solve this by string!

So we approach this by trying to make a knot out of it. We can only ever do an integer amount of twists, so this is what we imagine in our knot. so here a is just an integer, could be positive or negative. We then take it and slide it 90 degrees to get -1/a, fairly simple. now this twist a is vertical, so if we add twists, they won't directly add to this. Just to make the signs look good, we'll add -b to this tangle.