Midterms, Midterms, and The Curse of Handheld Computers.
It may seem a bit early, but midterm season is starting for us Eng Scis here at UT. Last week was linear algebra, yesterday was calculus, and today was physics. These tests ran the gamut from absurdly easy to impossibly hard. The easy one was physics. There were only three questions, and success basically came from using one's calculator correctly. The impossible one was calculus. There was stuff on that test that I had never seen before; and even though we got 110 minutes to do 11 questions (yes, that's 10 minutes per question), I barely finished. Well, truthfully, for the last question I just wrote down some random stuff. Perhaps somebody reading this will be able to solve this question:
Consider the function f defined on (0,1) by
f(x) =
/ 0 if x is irrational

\ 1/n if x = m/n
where m and n are integers without any common divisors. Prove that f is continuous at every irrational point in (0,1), and that f is discontinuous at every rational point in (0,1).
Pretty tough, eh?
Anyways, as you may have noticed from my last post, I brought a lovely threeyearold handheld computer (a Palm M505) from home. I'm afraid that this device is going to be my downfall, or at least the downfall of my marks. Anyone who has ever played the game "DopeWars" knows how addicting (haha) it can be. That game now fills the time before, after, and during lectures. My notes have become substantially shorter since the Palm came into my life.
Consider the function f defined on (0,1) by
f(x) =
/ 0 if x is irrational

\ 1/n if x = m/n
where m and n are integers without any common divisors. Prove that f is continuous at every irrational point in (0,1), and that f is discontinuous at every rational point in (0,1).
Pretty tough, eh?
Anyways, as you may have noticed from my last post, I brought a lovely threeyearold handheld computer (a Palm M505) from home. I'm afraid that this device is going to be my downfall, or at least the downfall of my marks. Anyone who has ever played the game "DopeWars" knows how addicting (haha) it can be. That game now fills the time before, after, and during lectures. My notes have become substantially shorter since the Palm came into my life.
1 Comments:
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