1.4 Properties of O-notation

Question 1

What is the rough hierarchy of functions from fastest to slowest growing

Answer 1

Question 1

How to avoid comparing functions based on definitions of O-notation

Answer 1

Instead use intuition based on the equivilance to the <= operator (usually works)

Question 2

When to use formal definitions

Answer 2

In edge cases or situations where you aren’t sure based on intuition

Question 3

How to use L’ Hoptitals rule to compare functions

Answer 3

Question 4

Example

Answer 4

Question 5

Using L’Hopital’s rule:

Answer 5

Question 6

Dealing with unpleasent exponentials

Answer 6