You basically have to know what the power series are for . Then you can just use substitution.
Determine the power series expansion of at without computing derivatives
(i)
(ii)
(iii)
So how the heck would I do this? If someone could show me step by step how to do one of them I'm pretty sure I could do the rest, but I don't know how to do it without derivatives as I would have just taken the taylor series