By the sound of it Mother Nature will be keen to get the ball rolling soon - 3cms is a good sign. And I hate to say it, but there is more chance of something going wrong with an artificial induction than there is from letting your labour start naturally. However, at 3cms, your chances of the induction having a successful outcome are increased. It is those who are induced with a firm or closed cervix or a dialation of 1-2 cms that have an increased risk of the baby becoming distressed as they are simply not ready for birth (the baby doesn't pay any attention to EDDs - Mother Nature is the artist and only when the masterpeice is complete will the baby wish to unveil itself!!). Ask your Ob what your score is on the Bishops Score Chart - this is used to determine the degree to which your body is ready for labour and the probable success of you being induced. The higher the number the better the probable outcome.

I know you've probably read it before, but remember that your EDD is an estimate at best and scans are not gospel. Its the system that gets it wrong - not your baby, your body or Mother Nature! The innate wisdom of these 3 factors combined overshadow anything that a person with a white coat or medical degree says to you.
38 - 42 weeks is a perfectly normal and healthy length for pregnancy (I doubt you would make it past 41 weeks by the sound of it) so try not to focus on Friday and just relax and listen to what your body is trying to tell you. Things are more likely to happen naturally that way and this is MUCH safer for you and the bub. Not to mention the contractions build up much more gently and slowly in a naturally induced labour so the baby remains calm and your ability to cope is much increased.
Have faith in your body babe - its smarter than you give it credit for.

Wishing & praying Mother Nature works her magic before Tues. All the best no matter what.
XX
Lol - just read your latest post. Thats awesome. Mother Nature has spoken and your baby is truely on its way. Wonderful news - all the best and enjoy your bub to be.