This problem asks you to review the lecture notes with the proof of the Laurent series theorem and address certain key steps, but in the context of an example function 1 f(z) = x+1 Note, this f(z) is analytic on |2| > 1. So, we can take R = 1, and any R2 >|2|. 252 25, i) Identify the integral around CD2. For the example f(z), you can find an integral bound so that its limit as R2 is zero. That is, this f(z) has no regular terms! ii) Identify the integral around CaD. Introduce the N-term finite geometric series and remainder sum. iii) Perform an index shift that results in the integral formula for the c-coefficient specific to the example function. You do not have to evaluate this integral. (Don't forget the factor of 1/2i - it got typo'ed in the lecture.) iv) Identify the remainder integral Q(z) specific to the example function. Give a value for M that works for this f(z).