the taylor series for e isExplain why Taylor's Theorem guarantees that we can use a Taylor polynomial to estimate the value of e to any degree fesired
I really have no clue on this one. We never talked about e in class.
You don't need to have, all you need is that you have done Taylor's theorem and know at least one form of the remainder for a truncated Taylor series and the general term of the series in question.
Now what you have to do is show that for fixed x the remainder can be made as small as you like by truncating sufficiently far to the right in the series.
CB