Its a use by date not a sell by date so its a guideline only..... fill a jug with water and put the eggs in it. If they float, they are off and need to be binned. Something to do with gas that gets produced as the egg decomposes.
You should find that your eggs are just fine ! As bushbaby has described, just carefully lower them into a pan or jug of water. If they float then they are probably *off* - this is because the shell is porous and as they age, the fluid inside the egg evaporates and is replaced by air. If they just *tilt* they are probably ok to eat, just getting a little old and if they lie on the bottom of the pan/jug they are fresh.
I was taught the above egg-testing method in school and it has always worked for me. I ignore the dates on the boxes as they could be wrongly telling me they are fresher than I thought too.
I hard boiled some eggs yesterday that were dated mid march. They floated but smelt fine when I peeled them. If you are making a cake though you need the freshest ones you can find.