Recent content by akoska

Urgent probability questions! Please help! How can 5 black and 5 yellow balls be put into two urns to maximize the probability that a yellow ball is drawn from a randomly chosen urn? I got: P(draw yellow)=P(draw yellow intersect urn1)+P(draw yellow intersect urn2) =P(draw...

1, but the sum of 1s is obviously not convergent.

How do I show that f(x)=sum (from n=0 to infinity) cos(nx)e^-nx is a continuous function? x is from (0, infinity) So, I need to show that the series converges uniformly. I'm trying to say that |cos nx e^-nx| <= |e^-nx| and use Weierstrass comparison, but I can't find a function M_n to use for...

Wait, sqrt(n/(n^4-2)) > 1/n^3/2, right? So it doesn't matter that 1/n^3/2 converges?

So 1. converge 2. no 3. no, sin(x) doesn't go to 0, so the series diverges Correct?

oh, sorry... first one: sum over n from n=2 to infinity 2. sum over x from x=1 to infinity 3. sum over x from x=0 to infinity

I'm having trouble determining whether these series converge or diverge. 1. sigma sqrt(n/(n^4-2)) I tried ratio test, but it gave me 1 as the answer (indeterminate) 2. sigma sin (pi/x) 3. sigma sin(x) I know that sin(x) is bounded... Any hints?

Hello, Can anyone explain to me what this is? I can't seem to find any good references on this. I'm looking into protein transformations from a helix structure to a catenoid structure through the Bonnet transformation (ie, alpha-helix to beta barrel transition)

Geodesics of hyperbolic paraboloid (urgent!) Help me find the geodesics of the hyperbolic paraboloid z=xy passing through (0,0,0). I know that lines and normal sections are geodesics. Based on a picture, I think y=x and y=-x are 2 line geodesics. Then, maybe the planes in the z-y and z-x...

yes, sorry, that's what I meant. No, you don't. I simply did not want to type an almost identical question out again, and then forgot to mention that you don't need uniform continuity. So, using the definition of continuity, every sequence {x_n} in D that converges, {f(x_n)} converges...

If D is a dense subset of R and f is uniformly continuous, prove that f has a continuous extension to R. I said: if x0 is in D, then f(x0) is continuous. Let x0 be in R\D. D dense in R--> there exists {x_n} in D s. t. {x_n}--> x0. {x_n} is a Cauchy sequence converging to x. f is...

Yes, but I think the 'appropriately defined a' is the catch. a can be any differentiable function, adn although i can show that |f'(t)| is a constant for certain a, how can I show it for all a?

How do I show |f'(t)| is a constant? I get to the part: |f'(t)| = lim(dt->0) |a(dt)/dt| where a is the function ||f(s)-f(t)|| =a(|s-t|)... and then I'm stuck

Ok, i see now. Thanks. I have another problem now... I found the solution to be a=exp(t)-exp(-t) and I need to find the inverse of a. Taking the ln of each side didn't help at all.

For part of a problem, how would I integrate: (e^2t+e^-2t+2)^(1/2) with respect to t I have no idea..., but I've tried integration by parts to start...