Q: App to remove active applications

No.

FYI: The vast majority of apps you see shown, are NOT running in the background. Rather, they are merely in their "last used" state.

Read this and you'll have a better understanding of the multi-tasking i/f in iOS: http://support.apple.com/kb/HT4211

Bolongo Bay wrote:

 

It seems like when these last used items are deleted, things speed up a little. 

 

Usually that's do to the placebo effect.

A good thing to try in this sort of situation is to reset the phone - press and hold the sleep/wake and home buttons  simultaneously until you see the Apple logo appear on-screen, then release the buttons and allow the phone to finish booting normally. See if it runs better after doing that.