✔ 最佳答案
Paul McCartney got it wrong.
I know. The lyrics really are "if this ever-changing world in which we live in, makes you give it a try". My suspicion is that, at that point, he cared far less about using polished (or even reasonable) grammar than in getting the scansion and syllable count right. Sometimes in lyrics, whether musical or poetic, rhythm is an overwhelming consideration.
Come karaoke night, I'm more likely to sing "this ever-changing world in which we're living". That sounds nearly the same, but it doesn't contain the error.
In formal circumstances, the preferred construction is "the world in which we live". That keeps the preposition and its object together, keeps the classification of "in" as a preposition, keeps us from ending a clause with a preposition, and it still keeps the relative pronoun close to its antecedent.
In informal circumstances, the construction "the world which we live in" has gained acceptance. The phrase "live in" is taken to mean the same as "inhabit" or "populate", acting as a transitive verb. This construction is called a phrasal verb. Under this interpretation, "in" is no longer a preposition. It is a complement that modifies the verb, giving it an idiomatic meaning different from the meaning of the base verb.
If the setting is formal or scholastic, then "the world in which we live" is correct. If the setting is casual, then simply make a choice. Put the "in" before the "which", or put it after the "live".
Just, please, don't pretend that you're Paul McCartney. Don't do both.