How can I calculate limits? Is there any algorithm?

0 votes
asked Apr 13 in Mathematics by poliq (5,880 points)
How can I calculate limits? Is there any algorithm?

3 Answers

0 votes
answered Apr 13 by Adf289 (46,340 points)
As far as I know there are no algorithms to calculate limits.

Also the standard complexity-theory arguments about why no such algorithm exists, we can also provide some practical examples of limits which are not well understood.

For the first part, go read Senia Sheydvasser's post in The Academic Space; one of his examples is that there is no algorithm for determining whether a series converges or not. So, we can’t even create an algorithm that tells whether there is a limit or not.

Obviously, if we restrict ourselves to just a restricted set of expressions, like rational functions, then the problem is tractable. But usually the reason we’re interested in a reliable algorithm is because the limit we want to take is complicated!

As a concrete example, the Euler–Mascheroni constant is given by a limit:

[math]\displaystyle \gamma = \lim_{n \rightarrow \infty} \left( - \ln n + \sum_{k=1}^n \frac{1}{k} \right)[/math]

But while we know this limit exists, and can approximate its value, we don’t know whether it’s rational or not!
0 votes
answered Apr 14 by costy (5,860 points)

Well, there is an awesome Limit Calculator that will definitely solve your problem, You see, it helps a lot calculate one-sided and two-sided limits, as well as limit representations. Each function calculation has a step-by-step solution so that you can easily understand how this problem is solved. During my college years I used it quite often and should say it worked pretty well for me. Simply give it a try

0 votes
answered Apr 20 by swipka777 (3,370 points)

There are a lot of different calculator opportunities and functions. As for me, I am currently using https://derivativecalc.com/ derivative calculator, which is a perfect solution for studying. It's very important to find a comfortable way to use for studying, so I am using a derivative calculator there. 

30,661 questions

33,112 answers

194 comments

1,089,807 users

...