1. ## Growth Condition

Hello all,

I'm working on a problem, that at the first step requires a growth estimate, that I can't seem to get. Here's the pertinent information:

Let $u\in C^2(\mathbb{R})$ satisfying
$\lim_{|x|+|t|\to\infty}\frac{u(x,t)}{|x|^5+|t|^5}= 0.$
Show that there exists $C>0$ so that
$|u(x,t)|\leq C(1+|x|+|t|)^5$
for all $x,t\in\mathbb{R}$.

Thanks for the help!

2. ## Re: Growth Condition

Maybe this should be moved to Differential Geometry. I never thought of Analysis as a subset of Differential Geometry, and just posted this in Calculus choosing the more relevant section-title, without reading the subsections. Apologies if it matters at all.