Stumble w/Throttle

[Kenneth]

On, my 200q20v,  I get a stumble if I give it too much throttle too quickly as the rpms rise, if I just give it too much throttle too quickly at a given rpm.

If I add throttle more slowly this doesn't happen, and it seems like after the stumble it sort of "clears its throat" and the power comes back.

It's not throwing any codes right now, but earlier, before a dead battery change, I was consistently getting a check engine light and code for "air/fuel ratio out of range."  I can't remember the specific code number or text right now, but I didn't change anything but the battery yet and the CEL hasn't returned. 

I suspect the symptoms could point to a boost leak.  Is there anything else that could be likely?

P.S.  Actually another footnote is that my coolant gauge isn't working.

Thanks,

Kenneth
(Sent on a Virgin Mobile Samsung Galaxy S® III)