Colocation only offers 1A with 1U service

I buy for colocation service (in the SoCal area).
But I find that most offer only 1A 110v service.
This seems far too low. I have a marsh standard HP DL360p server with 2 CPUs. Any CPU can exceed this 1 A power allocation, regardless of RAM, drives, fans and other overhead.
Idle it will probably be exactly the 1A budget, but switching on or under load will certainly exceed.
Even the most power-efficient 1U enterprise-class server has a 70 W CPU. Add the rest of the system and save money on the 1A Power Budget.

Do I miss something here? Is that a kind of wink, Nudge Nudge Limit? Is it 1A * 110V based on monthly usage (80 kWh)?
What happens if I go through for a short time?

As for My Needs: I'm just an individual looking for a reliable hosting service for a few games (like Minecraft), websites, and home-lab style tasks in a corporate environment. As such, I'm pretty price conscious, so buying a quarter table for my "hobby" is too bearable.

If someone with experience, especially hosting providers, can answer my questions, that would be greatly appreciated.
Many Thanks

real analysis – Find $ f $ on $[1,a]$ such that $ f ge x log x $, $ f $ is strictly convex and analytic, and $ x log x $ only touches $ n $ times.

I am looking for a function $ f $ defined on $[1,a]$ that fulfills the following:

  1. $ f (x) ge x log x $ on $[1,a]$
  2. $ f (x) $ is strictly convex
  3. $ f (x) $ is analytical
  4. $ f (x) -x log (x) = 0 $ just $ n $ Let's go $[1,a]$,

My attempt was to construct $ f $ as follows:

$ f (x) = x log (x) + 1 + g (x) $

from where $ g (x) $ would have oscillatory behavior (eg $ cos (x) $). Every time I try to add vibrations, I violate the strict conditions of convexity.

Calculus – What is the end result of this equation: -z * d / dz (1 / (1-a * z ^ (-1)))

Okay, I'm really confused about that because in the book the solution is the equation and book solution

Now the book uses the quotient rule for this distinction. Now I hate this rule, so I thought why not try the composition rule instead. The end result was different for me. I tried it with online machines and they gave the same solution that I got The solution from an online calculator

Okay, now I'm just confusing which one is right and I do not know if that helps, but the subject is z-transform for the course of digital signal processing.
Many Thanks