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Jan
10
comment Trigo function integral
@Dr.SonnhardGraubner But you have a sum of integrals, which is actually computable by elementary functions (see David Quinn's first comment). Integrate one by parts, and the other will simplify.
Jan
10
comment Trigo function integral
@Dr.SonnhardGraubner That's not the question.
Jan
5
comment How to Trace a Real-Life Flower Using Polar Equations?
"I am allowed"? Competition, exam? And you expect somebody will do your homework?
Dec
27
comment Is the absolute value of zero positive or negative?
And to add to the ambiguity, the usual meaning of "positive" alone is not the same in every country. In France, you usually say positive for $\geq0$ and strictly positive for $>0$. In anglo-saxon countries, I believe positive is $>0$ and $\geq0$ is non-negative. The best is to always be explicit. For $\geq$, it's also frequent to see "positive or null", at least in France.
Dec
24
comment Adding $\cos \theta$ and $\sin \theta$ of Perpendicular Vectors
You don't need to, but it may be a bit simpler. To make $v_x$ appear, develop the matrix product, and put apart the $\cos \theta$ coefficients (you will get $v_\perp$), and the $\sin\theta$ ones (show it's $v_x$).
Dec
24
comment Adding $\cos \theta$ and $\sin \theta$ of Perpendicular Vectors
You should find everything you need in these Wikipedia articles : Rotation and Rotation matrix. Notice that you are really interested in the vector expression of a plane rotation. Notice also that the coordinates of $v_x$ depend trivially on the coordinates of $v_{\perp}$.
Dec
16
comment Mittag-Lefflers's Theorem - The meaning of “having no interior accumulation point”
Yes, I changed my comment. Anyway, I think the OP didn't pay enough attention to this. Being in U is equivalent to being interior, when U is open. This has nothing to do with accumulation points.
Dec
16
comment Mittag-Lefflers's Theorem - The meaning of “having no interior accumulation point”
In the condition no accumulation point in $U$, the last two words are important.
Dec
16
comment Mittag-Lefflers's Theorem - The meaning of “having no interior accumulation point”
In the usual french definition, an accumulation point of a subset $A$ in a topological space $E$ need not be in $A$. That's the equivalent of limit point in english I believe. Is there another english definition for accumulation point?
Dec
5
comment Something fishy in the Zeta function
$\sin \pi=0$...
Nov
17
comment Proving $\int_{0}^{\infty} e^{-x^2}dx=\sqrt{n}\int_{0}^{\infty} e^{-nx^2}dx$
Change of variable $x=\sqrt{n}u$ in the first integral.
Nov
16
comment Prove that $1+x+\frac{x^2}{2}+\dots+\frac{x^n}{n!}<e^x$ for all $x\in(0,\infty),n\in\mathbb{N}$
The question is only interesting if your definition of the exponential does not depend directly on the power series. For example: $$e^x=\lim_{n\to\infty} \left(1+\frac xn\right)^n$$ For this definition, see math.stackexchange.com/questions/637255/…
Nov
15
comment How do you derive the formula of $\sin (a+b)$ from $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$
@avid By the way, I don't think MSE users can be expected to write a perfect english. This is the most widespread language on earth. The downside is, it's also the most victim of bad usage.
Nov
15
comment How do you derive the formula of $\sin (a+b)$ from $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$
@avid The three cryptic sumbols are called a smiley. I don't know what's Bernard mother tongue, but at least in french, "differentiate" is said "dériver", hence a possible translation mistake (see the first comment of the question you refer to). Since differentiating yields the derivative, even if wrong, it should be understandable (at least to me it was, but maybe I'm biased, since I'm french).
Nov
14
comment Evaluate $ \int_{1}^{\infty} \frac{\sqrt{x - 1}}{(x + 1)^{2}} ~ \mathrm{d}{x} $.
Honestly, with 1500 points I expect you know the customs here, and I see many answers where you used LaTeX. You could make an effort and write your answer correctly.
Nov
14
comment Finding an analytical expression for the eigen values
So simple when you see the trick! Very nice. And the eigenvalues of the tridiagonal matrix are indeed easy (there is a three term recurrence for the determinant).
Nov
13
comment Determine Fastest 3 horses out of 125 when only 5 racing track are given without using stopwatch?
And one on MO: mathoverflow.net/questions/50737
Nov
13
comment Determine Fastest 3 horses out of 125 when only 5 racing track are given without using stopwatch?
For three horses, there are several questions on MSE: math.stackexchange.com/questions/614772 math.stackexchange.com/questions/744473 math.stackexchange.com/questions/744559 math.stackexchange.com/questions/56159 math.stackexchange.com/questions/1361065
Nov
12
comment What is the period of $f(x) = \sin^4(x)+ \cos^4(x)$?
I don't see how your example is related to your first sentence. A constant function has any nonzero number as a period, thus it's certainly not at most $\pi$.
Nov
12
comment What is the period of $f(x) = \sin^4(x)+ \cos^4(x)$?
Generally speaking, the sum of two functions of period $a$ is not necessarily of period $a$. Just take $f-f=0$, for instance. Or less trivially, the difference of two trigonometric polynomials $f,g$ which have the same first few terms.