1 Question 2 Let I be the function defined by V(x) = Let In(x) = Volo...of(x) n copies but note that alternate definitions proceed by induction: Let VI(x) = V(x) and define Inti(x) = In(V(x)) or, equivalently, define Inti(x) = V(In(x)). 1. What is the domain of In for ne {1, 2, 3,4} ? 2. What is your guess for the domain of In in general? 3. Calculate V' (x) for n E {1, 2, 3, 4}. Arrange your calculation in a way to make it easily understandable. There are various approaches here and some are easier to understand than others. Do not be afraid to start on one approach and give it up in favour of an other. 4. What is your guess for In(x) in general. You are not asked to prove this by mathe- matical induction, but it is a good exercise to give it a try