2
votes
1answer
52 views

$|x|^{|x|}$ is continuous in $\mathbb{R}$

I'm trying to show this now my self, but still no go. There isn't really a concrete attempt that I can show.. Help?
2
votes
7answers
116 views

for $n$ an integer, why is $n^0=1$ ??

This is so going to cost me.... I was wondering why for any integer $n$: $n^0 =1$. Perhaps It's because $n$ is a round number and if $m$ is a non negative integer, also round then: $$n^m = 1 \cdot ...
0
votes
1answer
131 views

For what $ \alpha \in \mathbb R$ is $ |x|^\alpha $ differentiable in $x=0$?

I came across the following question: For what $ \alpha \in \mathbb R$ is $ |x|^\alpha $ differentiable in $x=0$? What I have tried: Since for $ \alpha = 1 $ is clearly non-differentiable in ...
5
votes
1answer
900 views

Prove variant of triangle inequality containing p-th power for 0 < p < 1

Sorry if this is a trivial question, but I am kind of stuck with proving the following inequality and have been searching for a while: $\rho \left( \sum\limits_i^n d_i \right) \leq \sum\limits_i^n ...