You should ask definitely. All drs are different. I'm also due the third and my Dr will induce me any time after Tuesday as long as my body and my baby boy are ready. Sometimes they won't unless there is a medical issue until you are going on 42 weeks. It really depends on your Dr.
I am due today and no baby!! I see my midwife on tuesday and if baby isnt here by then I will ask her about induction options. I do not suggest inductions as they increase your risk of a csection but I would still like to discuss it. I read ftm's like myself tend to deliver after 41 weeks so im debating on going into week 41. Your body will deliver when baby is ready :)