Recent content by samithie

I'm trying to show \sum_{k=1}^{\infty}2^{k}sin(\frac{1}{3^{k}x}) does not converge uniformly on any (epsilon, infinity) now I was able to show that it converges absolutely for x nonzero, by getting it in the form \sum_{k=1}^{\infty}x\left(\frac{2}{3}\right)^{k}\frac{sinx}{x} and so the sinx/x...

yes sorry about the typos. I think the directional derivatives is not the issue I'm just wondering about if I need to do this piecewise.

f: R2 to R1 given by f(x,y) = x(|y|^(1/2)) show differentiable at (0,0) so I'm using the definition lim |h| ->0 (f((0,0) + 9(h1,h2)) - f(0,0) - Df(0,0) (h1,h2)) / |h| so first for the jacobian for f, when I'm doing the partial with respect to y, do I have to break this into the case y>0...

thanks that's very helpful!

f is a continuous function on [0,infinity) such that 0<=f(x)<=Cx^(-1-p) where C,p >0 f_k(x) = kf(kx) I want to show that lim k->infinity ∫from 0 to 1 of f_k(x) dx exists so my idea is if I have that f_k(x) converges to f(x)=0 uniformly which I was able to show and that f_k(x) are all...

Does anyone have a good book or reference on computing riemannian connections. I'm looking at Do Carmo and can't find any examples. For ex. If X = y(d/dx) + x(d/dy) + w(d/dz) -z(d/dw), Y = z(d/dx) - w(d/dy) - x(d/dz) + y(d/dw), Z = w(d/dx) + z(d/dy) - y(d/dz) - x(d/dw) being the classical...