Recent content by slearch

cross product isn't defined for dimensions higher than three, so you would just prove it for three space.

i could be wrong but i think that theorem only applies to bounded functions.

use the quadratic formula

By the way it's worded it looks like your cost will depend on the total surface area of the closed cylinder - that is twice the area of the circles and the area of the rest. That part about the cost being n times the circumfrence also seems ambiguous - I can't really tell if they want the total...

The diagonals of the parallelogram are precisely a+b and a-b. if you are talking about proving your equation above, multiply it out, keeping in mind: (a+b)\cdot (a-b) = a\cdot a - b\cdot b + b\cdot a - a\cdot b edit: fixed my mistake

a) This looks right. You should get the same number as when you look at -\int_{-\infty}^0 e^x dx Do you see why? b)What steps did you go through here? c) I don't know whether this is undefined, but I do know that \lim_{x\rightarrow\infty}\arctan (x) = \frac{\pi}{2}

I think it means that the probabilities on the left are a non-increasing sequence converging to the number on the right (that's what you have to prove).

Continuity of ln away from 0.

It looks like the y's became x's between these two steps :)

This is the order one usually does it in. I can't imagine skipping Algebraic Topology - there are too many key things there and there is a large interplay between it and differential forms.

glad to help :)

F_x is the partial of F with respect to x, yes.

And to do this, you should think about what the properties the normal vector to a surface might have.

No, Ax + By + Cz = D is the equation of a plane, a very specific type of surface. This question asks you to prove it for any surface of the form F(x,y,z) = 0. You first need to find the equation of a normal vector to the surface, then work on what \gamma might be.

The point is that it doesn't matter what the surface is, the equation should hold for any F(x,y,z) with continuous partial derivatives.