I have a problem about question #4. I know that statement is true and I used limit techniques. I know that according to limit tech. if lim x-gt;...

I have a problem about question #4. I know that statement is true and I used limit techniques. I know that according to limit tech. if lim x-> infinity f(x)/g(x) = 0 then f(x) is in O(g(x)). However, I am not sure that my proof is acceptable or not. a3.pdf is the assignment and 4.docx is my solution.