By searching through wikipedia, I’ve got An analytic function is a function that its Taylor series at any point x_0 in its domain converges to the function itself for x of x_0. It means that if a function is analytic at c, it can be expanded to the Taylor series centered at C, like e^{x}, it can be expanded analytically. Therefore, the differences between Analytic function and infinitely differentiable is that the previous one can expand into power series representation  but not every infinitely differentiable function can be expanded into every x.

After reviewing the midterm that I have already taken in February, I generalize following details that I still need to improve.

1. Calculation of Integration, which means I’m not familiar enough to solving the integration problem, not merely lacks of practices but generalize the types of integration problem.
2. Way of approaching problem, even though I was done a so-so job for the questions expect #1, but after reviewing the steps that provided, I am still not enough for mathematical logic.
3. Managing time; I’m not reasonably manage my time during exam, which caused I don’t have enough time to review the whole exam sheet.