# List of speeds of functions?

1. Aug 16, 2015

### RyanTAsher

1. The problem statement, all variables and given/known data

Can you create a list of which functions increase towards infinity the fastest for limit solving?

2. Relevant equations

3. The attempt at a solution

I'm trying to make a list from least speed, to fastest speed, in approaching infinity.

As in, if you have a limit, and it has multiple types of functions, which function will be the largest, fastest.

I tried making my own little list, but I'm not sure how accurate it is, or if I'm missing any functions. Also, I'm not sure where trig functions would fit onto this list, or if they even do, because they oscillate. I'm just trying to make this for a friend.

Logarithmic > Square Root > Algebraic > Exponential ?

2. Aug 17, 2015

### StrongSpica

You can use asymptotic analysis if you know how to.
You may also include in your list Power functions between Algebraic and Exponential, and Nth root between Logarithmic and Square Root.

3. Aug 17, 2015

### Zondrina

There are lots of different functions depending on what you want to consider. Trouble will arise when making a list if you consider multiple factorials and exponentiations.

Maybe a starting point for a list would look something like:

$$\text{log}(x) < \text{log}(x \text{log}(x)) < x^n < b^x < x! < x^x$$

This barely covers a list of functions, and I'm not sure the list is what you are looking for.

For a more complete list of functions, see: https://en.wikipedia.org/wiki/List_of_mathematical_functions

4. Aug 29, 2015

### RyanTAsher

Thank you, I appreciate it, I was just looking for a basic list that encompasses everything one should know at a single variable calculus level!