Study! Study! Study! Study!

Okay, this either needs a futa tag or needs the 3girls tag knocked off.

The middle one is a BOY, this CG is from Kanojo-tachi no Ryuugi, one of my favorite eroge ^_^; Sorry, guys. #girls tag is failed.

I think that's what the pseudo math is trying to prove, that middle g(x) = L, just like the other two. But this fails in my book because of bad math, and because I don't mind yuri

This isn't entirely bunk math. It's just an extension of logic; if f and h are bounds on g, and converge to one point at a particular x, then g must lie on that point (L). It's sort of like the Squeeze Theorem, appropriately enough.

A pre-calculus theorem:
http://en.wikipedia.org/wiki/Sandwich_theorem
By the way, the graphs on the right of x = a do not satisfy f(x)≤g(x)≤h(x) (it actually is the reverse), but the conclusion is still correct.