The problems in the file submitted are from an undergraduate course in real Analysis. If you are able to work the problems, please detail any theorems or lemmas used in your solutions. The book we are using is titled "The Elements of Real Analysis" by Robert G. Bartle. We are working on derivatives and integrals, but have not started infinite series.
(a) Answer: 0
From the definition of g(x), we know, when 0<=x<1/3, g(x)=0 and
thus dg=0; when 1/3<=x<=2/3, g(x)=1 and dg=0; when 2/3<x<=1, g(x)=2
and dg=0. So dg=0 almost ...
This provides examples of evaluating integrals.