# Catalog of limits

WARNING: This post contains hundreds of mathematical formulas. Do not open it on devices, where rendering of MathJax is slow!

For more comprehensive catalog see https://mathindex.wordpress.com (it includes more limits, series, finite sums, and recurrences).

This is an attempt to organize questions about evaluation of common limits. Discussed at Catalog of standard exercises

### Trigonometric limits

• I'm scared... :-( – Asaf Karagila Sep 1 '14 at 21:32
• @AsafKaragila Main reason I went ahead with this is to see what problems will appear with such a list, and thus give more concrete input to discussion in the other thread. This is just an experiment... script time is cheap. – user147263 Sep 1 '14 at 21:48
• I don't like this! My laptop can't load more than 5 of them without freqqzin up!!! I cny even type properly.pleaseleae condense into eperate links(put all 100 in a nother linkP – user142198 Sep 2 '14 at 0:15
• @user142198 I was afraid of that... Not sure what a solution could be: moving the catalog to a site where formulas are rendered as images (would that even help?) or splitting the answers into much smaller chunks, so that they get paginated (only 30 answers are displayed at once). – user147263 Sep 2 '14 at 0:17
• If the sets were all contained in seperate links I would only need to render seta of 100 by choice, I think I m loadin 500 atm – user142198 Sep 2 '14 at 0:18
• As in have each o these answers redirect to a separate page with thelists(so yes smaller chunks), does spoiler code stop the rendering untilscrollover? – user142198 Sep 2 '14 at 0:21
• ybe these statistics arehelpful in knowing how many you want to put on the page: it takes 46sef to load first 44,84sec for 118total, 144sec for 269 otal. I have 1gb ram dual core 1.6ghz – user142198 Sep 2 '14 at 0:34
• The above numbers were amount of time elapsed since page refresh and the right was number of lines of latex had rendered thus far. Sorry if that was unclear(this was written and pasted from notepad). – user142198 Sep 2 '14 at 2:06
• +6 for your effort... – draks ... Sep 2 '14 at 6:08
• I think it would be better if the posts about the same limit were grouped together (even if they are not exact duplicates, for example if they require some specific method, or avoiding some method). For example this limit is three times in one of your lists: math.stackexchange.com/questions/36299/…, math.stackexchange.com/questions/420698/… and math.stackexchange.com/questions/552016/… These 3 occurrences are quite far from each other. – Martin Sleziak Sep 2 '14 at 12:00
• I suppose the ordering is by question id at the moment? It would not save that much rendering, but we could do this: $\lim\limits_{x\to0}\frac{1-\cos(x)}{x}$ 1, 2, 3 – Martin Sleziak Sep 2 '14 at 12:03
• @MartinSleziak The order is by ad-hoc "hotness points", equal to 20*(total score of answers) plus the number of views. When the same limit appears multiple times, the first appearance should be the canonical one. Rearranging them by hand isn't in my plans; the idea was to make content better accessible with an automatic tool. – user147263 Sep 2 '14 at 12:12
• BTW some links (probably generated by some automated process) see to be incorrect. For example, one of the answers contains a link like this: $\displaystyle \lim\frac{\sin x}{x}$. It links to question about $\lim\limits_{x\to+\infty}\left(x-x^2\log\left(1+\frac{1}{x}\right)\right)$ (BTW maybe we could move the discussion to chat, so that we do not put too many comments here.) – Martin Sleziak Sep 2 '14 at 12:15
• @MartinSleziak They are marked community-wiki. Feel free to edit, though you might find the process pretty slow. After seeing how these look and perform, I don't think I'll keep adding to this thread. Putting also logarithmic limits, exponential, square roots, rational functions... would make browsing next to impossible. I'll try to come up with a better system outside of SE. This thing can sit here as far as I'm concerned. – user147263 Sep 2 '14 at 12:45
• @MartinSleziak Don't worry about that. If I get tired of pings, I'll ask for disassociation, but so far this isn't a problem. – user147263 Sep 3 '14 at 14:43