# What is Limits: Definition and 999 Discussions

Els Límits (Catalan pronunciation: [əlz ˈlimits]) is a Spanish village, a civil parish of the municipality of La Jonquera, situated in the province of Girona, Catalonia, in Spain. As of 2005 its population was of 115. Its Spanish name is Los Límites.

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1. ### I What's my mistake in this integration problem?

Here's the problem: ##\int_0^{2\pi} \cos^{-1}(\sin(x)) \mathrm{d}x## If I do the substitution ##u = \sin(x)##, both the limits of integration become 0 and the integral would result in 0. But the graph of the function tells me the area isn't 0. Where am I going wrong?

10. ### Medical Does the human brain really have a limit for memory storage?

I recently read that the “functional information content of human memory" as 10^9 bits at midlife based on testing of text and image retention” It makes sense that anything biological would have a limit but memory is such a strange thing that I can’t see how it would be like storing bytes on a...
11. ### L’Hôpital’s Rule for indeterminate powers

For this, Does someone please know why we are allowed to swap the limit as x approaches zero from the right of y with that of In y? Thank you for any help!
12. ### Radii of stacked circles inside the graph of y = |x|^1.5

(a) The hint from question is to used geometrical argument. From the graph, I can see ##r_1+r_2=c_2-c_1## but I doubt it will be usefule since the limit is ##\frac{r_2}{r_1} \rightarrow 1##, not in term of ##c##. I also tried to calculate the limit directly (not using geometrical argument at...
13. ### General form of Newton II -- Not understanding this step in the derivation

For this, Does someone please know how do we derive equation 9.9 from 9.8? Do we take the limits as t approach's zero for both sides? Why not take limit as momentum goes to zero? Many thanks!
14. ### Why Can We Take Limits of Both Sides? [Answered]

For this, Does someone please know why we are allowed to take limits of both side [boxed in orange]? Also for the thing boxed in pink, could we not divide by -h if ##h > 0##? Many thanks!

47. ### I Limit of limits of linear combinations of indicator functions

I have a sequence of functions ##0\leq f_1\leq f_2\leq ... \leq f_n \leq ...##, each one defined in ##\mathbb{R}^n## with values in ##\mathbb{R}##. I have also that ##f_n\uparrow f##. Every ##f_i## is the limit (almost everywhere) of "step" functions, that is a linear combination of rectangles...
48. ### MIT OCW 8.02 Electromagnetism: how were these two limits calculated?

I know what the answers are, because this is all part of the notes from MIT OCW's 8.02 Electromagnetism course. In case you want to see the actual problem, it is example 2.3 that starts on page 18; the limits I am asking about are on page 20. How do I go about calculating the limits? Ie, what...
49. ### A Limits and Supremum: Is It True?

We have ##a_n## converges in norm to ##a## and a set ##S## such that for all ##n\ge 0## $$\sup_{s\in S} <a_n,s><+\infty .$$ Is it true that ##\sup_{s\in S} <a,s><+\infty##
50. ### I Limits of Two Ordinal Sequences

Let ##\omega_1## be the first uncountable ordinal such that ##x## is an element of ##\omega_1## if and only if it is either a finite ordinal or there exists a bijection from ##x## onto ##\omega##. I want to define a matrix such that the matrix contains each element of ##\omega_1## only once. To...