When an function is analytic at c, we can find a Taylor series at point c such that the series converges to f(x) for x near c.This definition is useful because it can change a function into a infinite power series. e^x is an example for this, it is infinitely differentiable and the Taylor series is still itself.

An analytic function can be differentiable infinitely. However, a function differentiable infinitely does not mean it is analytic. Therefore, by determining if all nth derivatives are zero, we can distinguish whether an infinitely differentiable function analytic or not.

Name: Rain Xia       Student Number: 59118159

I think the most difficult question on the midterm is the question #5. I am not very familiar with those volume questions at that time. The volume questions could be pretty challenge to us because we need to think out a rotating graph or cut the object into empty cones by ourselves. I realized how to do this kind of question recently.

Tips:

1. More practice, do all the pre-reading questions, all the practice question that teacher gave us, and don’t lose points on the calculation part.
2. Really understand the basic definition of some key words.