prove the language is regualr [closed]


I have 2 questions that I was required to tell if the language is regular or not. I have the answer so I know that the answer for both of them is true. But I don’t have the intuation why and I can’t think of how to build automate or equivalnce class. it seems that the states are inifinte.

  1. I have regular L, and I have L’: {x: there is y such that |y| = |x| and xy belongs to L}. why L’ is regular?
  2. I have the language L2 which is all the words w such that for each sub-word u of w -10<= amount of a in v - amount of b in v < 10 ( the diff between amount of a and amount of be is at most 10). why L2 is regular