Gimme fried chicken

A great success on test question 1 after only one day's work. Getting out of the house [to see people and spend an hour with my student] must have been good for the brain. I'm slightly peeved at the trickery of this question - it's an epsilon-delta proof at heart, but after I've spent so long learning how to do such proofs "properly" [by manipulation of inequalities], this particular question turns out to be better done by cheating methods. Specifically, expressing the tricky part of it as some other variable and then fiddling around until the obvious becomes even more obvious. I feel rather let down.

However, I still haven't managed to prove that (xy²)/((x² + y²)^3/2) ≤ 1 for all real x and y, so I suppose I shouldn't be complaining. It's a lemma left over from several assignments ago. I told myself I would assume it for now and prove it properly later, but I never got around to doing so.

I've noticed that as I work further into mathematics, my study habits are getting more and more relaxed. I'm studying both more and harder, but I'm less anal about having everything just right in my study area. For example, I can do maths with non-classical music playing now. I never used to be able to do that. This morning I worked to the sound of a particularly excellent country/blues compilation which I just acquired. Unfortunately my mind has latched onto a certain couplet and refuses to recall it correctly, so I'm walking around with a constant loop of "birds swim / fish fly / lovers leave by and by..."