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10h
comment Can the GM-AM inequality fail on a digital computer?
Not exactly a "minimal" example, but something will go wrong if $x$ and $y$ are so large that $xy$ overflows but $x+y$ doesn't.
1d
comment $ \lim_{x \rightarrow \infty} e^{1/x} = a $ is not equivalent with $ \lim_{x \rightarrow \infty} a^x = e$?
You should edit the title as well.
1d
comment Problem with simplifying $\frac{(3+h)^2-9}{(3+h)-3}$
@CiaPan: Probably $(3+h)^2 = 3^2 + h^2$...
1d
revised Finding whole number answers from whole number inputs
edited tags
1d
revised Explanation of derivation made at wikipedia.
edited tags
2d
comment Why does the Harmonic series diverge?
The title doesn't reflect the actual question...
2d
comment Is it possible to approximate $cos(x)$ with a linear combination of Gaussians $e^{-x^2}$?
If you're willing to use many Gaussians that are close to each other, then any function can be approximated by Gaussians; see Approximate Approximations by Maz'ya and Schmidt: amazon.com/…. But it seems this is not quite what you need. (It would perhaps be easier to answer if you told us what your purpose with the approximation is.)
Jun
28
comment Why doesn't L'Hopital's rule work in this case?
@user251125: This article by Boas might be of interest: maa.org/programs/faculty-and-departments/…
Jun
28
comment substitution rule and differentials
Similar questions have been asked here many many times. You may start here, for example: math.stackexchange.com/questions/21199/…
Jun
27
comment Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$
For the record, here's a spin-off question on MO: mathoverflow.net/questions/210167/…
Jun
27
comment Calculate $\int\int{\sqrt{1-x^2-y^2}}dxdy$ the domain is $x^2+y^2 \le x$
@satishramanathan: $a^3 = - (a^2)^{3/2}$ if $a < 0$.
Jun
27
comment Prove that $\sin^{2}{\theta} + \cos^{2}{\theta} = 1.$
What if $\theta$ is outside the interval $0 \le \theta < \pi/2$?
Jun
25
comment Why does a line integral not depend on the parametrization you use?
If line integrals are included in your course, the proof of this fact should be in your textbook (immediately after the definition of line integrals, presumably)...
Jun
25
answered Verify my solution of $y'=(1-y)\sqrt{y}$
Jun
25
comment Integral with complex variable
It looks divergent (decays too slowly as $y \to \pm\infty$). Why do you need to compute this?
Jun
24
comment What does a * mean after a letter signaling a result?
What's so confusing with that? The definition of equilibrium is that $dF/dt=0$. All they are saying is that the equation $w(F)F(1-F)-vF=0$ has two solutions; one is clearly $F_1=0$ and the other one (call it $F_2$) is the solution of $w(F)(1-F)-v=0$, and they claim that $F_2$ is positive. It's perhaps slightly confusing to denote both $F_1$ and $F_2$ by the same symbol $F^*$, but they do explicitly state that they are talking about two different equilibria, so that shouldn't need to cause any problems.
Jun
24
comment What is the probability of two rolling dice?
The question in the title is not the same as the question in the text. ;-)
Jun
23
comment Smart coordinates for six-dimensional integral
Not that I have tried, but perhaps you could use ordinary spherical coordinates for $\vec{x}_1$, and then for $\vec{x}_2$ use rotated spherical coordinates whose "$z$ axis" points in the direction of $\vec{x}_1$?
Jun
23
comment Calculate the sum $\sum_{n=0}^\infty\frac{1}{(4n)!}$
Or this one, for that matter: math.stackexchange.com/questions/1193695/…
Jun
23
comment Calculate the sum $\sum_{n=0}^\infty\frac{1}{(4n)!}$
Answer: (1) Search this site for "(4n)!". (2) Find this question: math.stackexchange.com/questions/221519/…. (3) Put $x=1$. ;-)