this was a post i did on another thread. this might help you. it helped me.
if your using everything on stock with the galaxy s3 i recommend you putting the background processes on "no background processes".
go to settings ,developer options.
it also has the option right above limit background process called do not keep activities. that kills all apps that you enter so you dont have to back out of everything. so there is no need to install a task killer on the galaxy s3.
and i do have another tip for you all out there... if your using a downloaded home replacement launcher, a way of putting a task manager widget on your phone is, long press the home screen , go to shortcuts,activites, then scroll down to task manager... there you go, there is no need to download one from the android market,google play whatever it is now. some people out there think it doesnt come with one but it does.just hard to find lol.