It's good to push things to the limit when you're rock climbing or running a 5K but the derailleur on your bike should stay well within it's set range. The upper and lower limits of your derailleur dictate the minimum and maximum of your gears and make sure the chain doesn't fall off your cartridge. There comes a time either after a bicycle overhaul, after a tough spill, or after just months and months of riding that the limits will need to be reset. Climb the rock of setting derailleur limits with these steps.
To set the lower limit first locate the two screws on the derailleur and tighten the bottom (or screw marked with an "L") as tight as it can go. Next pedal slowly and shift the gears into the lowest possible, usually the second largest ring on the cassette. Next wind out the cartridge and loosen the "l" screw until the chain slips into the largest ring without clicking or slipping. Once the chain goes in you've successfully set the rear low limit.
Set Rear High Limit
In much of a similar way as the low limit was set, tighten the top screw on the derailleur all the way to start setting the high limit. Once tightened pedal and shift so the chain moves its way towards the end of the cassette, the smallest rung. Loosen the screw again until the chain pops into the last run without any issues or hiccups. If the chain refuses to slip in it may be necessary to adjust the black oval clip known as the barrel adjuster.
Once you've set the high and low limits, it's time to set enough clearance so that your system can shift without any issues. There is a long screw sticking up that can be turned clockwise to open the gap and counter-clockwise to decrease it.
Setting the derailleur limits is often the first step in indexing your bike's gears and performing other chain or cartridge maintenance. Once you've mastered this step fine-tuning your bike's shifting becomes a downhill process.