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Aug
22
comment Proof for parallelogram law of vector addition
Vectors are a purely mathematical construct. You seem to be asking about the superposition principle, which is the physical fact that forces add like vectors. Don't get it backwards! You seem to be implying that vectors add like they do because of the superposition principle, but it's the other way around: we represent forces with vectors because addition of forces is just like addition of vectors. In any case, I think you should make your question clearer, because apparently no one understood what you were asking.
Aug
22
comment Where does this sequence $\sqrt{7}$,$\sqrt{7+ \sqrt{7}}$,$\sqrt{7+\sqrt{7+\sqrt{7}}}$,… converge?
This is fine if you've proved it converges, but I'm not sure OP has done that.
Aug
22
comment Proof for parallelogram law of vector addition
Two things. One, this is a mathematical question, so experimental evidence is not really a proof. Second, how do you define vector addition?
Aug
11
comment Rigorous treatment of expressions with differentials in physics books
Something to note, more or less echoing what littleO said, is that while sometimes this kind of thing can be formulated more rigorously using derivatives or differential forms or whatever, I find that thermodynamics is an area where it helps to think of differentials as really small quantities instead of a more formal alternative.
Aug
8
comment What is this expression means? $\sin^{-2}x$
@MichaelGaluza: Some people use $\sin^{-1} x$ to mean $\arcsin x$, that's the point.
Aug
7
comment Distance covered by integrating the Velocity of a Body
Most likely your calculator is set in degrees instead of radians.
Jul
31
comment Maximum value of $f(x)=\frac{x^2}{x^3+200}$ over natural numbers
It should be mentioned that this works as long as $f$ has only one maximum, too.
Jul
29
comment $\int_{-\infty}^{\infty}e^{-\pi x^2}\cdot e^{-2\pi ix\xi}dx = e^{\pi\xi^2}$
Hint: Complete the square in the exponent.
Jul
1
comment Transforming matrices using tensor transformations?
Well, it cannot be just replacing the coordinates, because the transformation law is telling you that you should multiply by two other matrices in addition to replacing $x$ and $y$ by their polar expressions (which is implicit in the transformation law).
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". (...)
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.
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 $\sin x = (e^{ix}-e^{-ix})/2$.
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 $(-1,1)$?
Oct
8
comment How do I take the limit of this function?
You must be doing something wrong: when I put in $2.1$, $2.01$, $2.001$, I get $15$, $150$, $1500$, etc.
Jun
16
comment Using dimensional analysis to evaluate $\frac{d}{dx}x^n$
@tpb261: I feel like the issue here, this being a man site and all, is showing that you can't make a non-constant dimensionless function out of only $ x $. For all we know, there might be a constant $ a $ with dimensions of length such that $ c =x/a $.
Jun
16
comment I can't quite figure out this “separable equation”
Small correction: having $\ln x$ in the equation already tells us that $x \neq 0$. Instead, you should assume that $x \neq 1$ so $\ln x \neq 0$.