Platformer background size - iPad

I've read a few posts that say large backgrounds should be cut up and tiled. Other say there are size limitations. Basically, I would like to understand the limits and what's the best practice for using large background image(s).
How big can a single image be for an iPad background? Must it be cut up and placed together on the scene?
Anything else I should know?
How big can a single image be for an iPad background? Must it be cut up and placed together on the scene?
Anything else I should know?
Comments
Out of curiosity, GS will process an entire image even if only a small pieces is on screen. If this is accurate, would FPS increase if the image was cut up so GS would not have to process 1024 x 1024 every single frame? Or can it handle this on an iPad no issue?