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Jun
12
comment What are “instantaneous” rates of change, really?
(...) With this point of view, the limit is not a process that will never end. Instead, it's an indirect way of specifying (without ambiguity) a number that you couldn't otherwise calculate. Maybe this will help.
Jun
12
comment What are “instantaneous” rates of change, really?
Maybe you should try not thinking of limits as movement, because then, as you say, you never "get there". Rather, when you see a limit like the derivative, imagine that there is a number that you cannot calculate, but that you can approximate with arbitrarily high precision. This is not some fuzzy thinking that cheats by evading the concept of instantaneous rate of change; if you can approximate a number arbitrarily well, then you know exactly what it is, even if you cannot calculate it "directly". (...)
Mar
19
awarded  Popular Question
Mar
11
awarded  Popular Question
Feb
19
awarded  Popular Question
Feb
15
comment Examples of apparent patterns that eventually fail
Sorry for being three years late, but I don't see what the deal is with the $\sqrt{163}$ sum. I mean, it's pretty cool, but what does it have to do with the question?
Feb
13
comment How is SO(2) compact according to this definiton?
MathWorld's definition doesn't make a lot of sense, because usually you can't cover the whole group (or manifold in general) with a single coordinate chart.
Jan
26
awarded  Nice Question
Jan
12
awarded  Good Answer
Dec
15
comment How to calculate$ \int_0^{\infty} e^{-x^2} \sin x dx$ in the most simple way
@Lucian: My comment is not as useful as I thought it would be. It would work if the limits were $\pm \infty$ (of course, the integral would be zero), but it doesn't work here because after completing the square, the limits of integration are not simple. It does let you get to the Dawson function quickly, but I thought you could get a closed form solution.
Dec
15
comment How to calculate$ \int_0^{\infty} e^{-x^2} \sin x dx$ in the most simple way
Use $\sin x = (e^{ix}-e^{-ix})/2$.
Dec
13
awarded  Nice Question
Nov
25
reviewed Approve Consider the following limit: $\lim_{n \to \infty } \frac{\ln(1+n)-\ln(n^{2})}{\sin(1/n)}$
Nov
13
accepted Does the matrix exponential take open sets into open sets?
Nov
13
comment Does the matrix exponential take open sets into open sets?
@m.g.: Well, that was simple. You should post that as an answer.
Nov
13
comment Does the matrix exponential take open sets into open sets?
@Jack: what about $x^2$ on $(-1,1)$?
Nov
13
asked Does the matrix exponential take open sets into open sets?
Nov
6
awarded  Nice Question
Oct
24
awarded  Yearling
Oct
23
awarded  Notable Question