I have several questions concerning different parts of the question:
a) Is it sufficient to show that ${1, e^x,...,e^{nx}}$ are linearly independent over the vector space of differentiable functions on R?
b) For part b, I don't quite understand what it means by "unique solution". Are we supposed to find the unique $a$? If that's the case, any suggestion on how to find it?
c) So I should be looking for something like this: $\mu= e^{-t/n}$? Why is "equally spaced" important in this problem? Thanks!
