Is my MagSafe covered under my MacBook's AppleCare? I have a white 2010 MacBook, and the outer casing for the wire on the MagSafe power adapter has developed a small split. Is this something that may be covered under my MacBook's AppleCare? Is it something that a genius might give me a "one time exception" for?
Troubleshooting MagSafe adapters

Whether your product is in or out of warranty, you can take your adapter to an Apple Authorized Service Provider or Apple Retail Store for evaluation and replacement if necessary. Pending the results of the evaluation, you may or may not be eligible for a replacement adapter free of charge. Signs of accidental damage would negate any coverage. Be sure to bring in the computer used with the adapter; it is required to process potential adapter replacements.

So there are competing things at play. If your cable is otherwise pristine, no bends, no mars, no scuffs and it's clearly not worn - you might think that this split could be caused by either abuse/nick/cut/carelessness or perhaps not holding up as designed. If the rest of the adapter cord is worn and starting to show normal signs that it's just wearing out (no cord lasts forever, especially when wrapped, unwrapped, tugged) you might be asked to pay for a replacement if it's not clear the physical separation was a defect in manufacturing.
If Apple didn't make the cable correctly, it's likely it would fail immediately, but the longer the time that passes until you take it in for service, it's more likely to be an external force causing the tear. Usually by inspecting the rest of the cable (not pictured) you will see other signs of excessive force so absent those signs of stretching and tearing, this might be covered despite what looks like an obvious cut/rip due to a tug.