Week 9

This week we learned about exercises of big-Oh proofs, and  proof of big-Oh using limit techniques.We also had a term test which I felt I did well on because Assignment 2 had really prepared me for the test, as I had to study the material and practice my knowledge for the assignment. For the Big-Oh proof it's mostly about using the definition. So, picking a c large enough, based on the highest-order term's constant factor can sometimes work. Another tip that was given was to plug in   n = 1 in order to potentially get an appropriate c and B. I learned an interesting technique to find c when proving an Upper Bound. You start with the upper bound on the top and try to make it smaller, then you put what you try to prove (the lower bound)  on the bottom and try to make it larger. Then you find a c that connects both bounds. I learned about proof of big-Oh using limit techniques which I found somewhat confusing because of all the steps you have to make and then the fact that you have to connect this information you found to the definition of limits and big-oh. When looking back at the slides, I do see they give a strategic way to try to use limits in the proof; prove the limit ratio equals infinity using some math, then translate the limit into its definition with c and n', then relate this definition to the definition of big-Oh.