Recent content by foxjwill

Try thinking about this equation right here. Remember that both \mathbf{p} and \mathbf{q} are vectors, while n is a scalar, so the "*" is scalar multiplication. But scalar multiplication can be rewritten using matrix multiplication, right? And once you write it in that form, try looking at its...

I'm currently trying my hand it this guy, but you might consider also posting this on the advanced physics part of the homework subform. These are the kind of manipulations physicists eventually become quite adept at doing. EDIT: Alright, I got it. Try substituting your expressions for...

Are you sure you wrote down the problem correctly? As micromass pointed out, whether or not A is closed is irrelevant. Maybe you have to show that 0<d(x,A)<\infty for all x\notin A?

Let's check this using x=17: \frac{(2\cdot5)\mod 2}{2} = \frac{\mathop{\mathrm{remainder}}(10,2)}{2} = \frac{0}{2} = 0, while 5\mod 2 = \mathop{\mathrm{remainder}}(5,2) = 1. Evidently, the two expressions are not the same. Can you see why this is?

Here's how you'd write your integral using LaTeX: \int_0^2 \sqrt{65 e^{2t}} dt which, when enclosed by "TEX" and "/TEX" (with the quotation marks replaced by square brackets), gives \int_0^2 \sqrt{65 e^{2t}} dt Anyway, try using the fact that \sqrt{a}=a^{1/2}.

Please try reposting this in the physics part of the forum.

Think of y as a constant (which is what it is). It might help to use a different letter, say \alpha, instead of y for the time being so you don't accidentally forget it's not a variable.

Correct. This is incorrect. Each part of the equation hk(af+bg)=hk=f-yg was derived by directly applying noncontradictory definitions (namely (i) af+bg := 1 and (ii) hk := f-yg), so you won't be able to get a contradiction without doing something else.

Multiplication is defined component-wise.

Try asking this in one of the physics subforums.

Almost. What you need to do is show that no matter what point x you choose from the intersection C_1\cap C_2, you can find a basis set C_3 such that x\in C_3\subseteq C_1\cap C_2. The standard topology on the real line is the topology generated by the open intervals (a,b); i.e., a set U is...

Well, you could use the fact that \nabla V is a path-independent vector field.

First of all, this is not text messaging, so please use full words. Anyway, this is correct, the distance is \sqrt{x^2+y^2}. Now, what you want to keep in mind is that the 'r' in polar coordinates is defined to be the distance from the origin--in other words, r=\sqrt{x^2+y^2}.

When you do get back to it, answer this: What is du when u=1+e^{-x}?

Nope. Let me ask you this: If I give you a point (x,y), can you tell me how far away from the origin it is? Also, remember that dx\,dy = r\,dr\,d\theta, not dr\,d\theta.