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Dec
16
asked Limit of $e^x/x^3$ at infinity without l'Hopital
Dec
7
comment Is $|\ln|x||$ differentiable?
@EkaveeraKumarSharma Not really a cusp. It's a jump (of 1st order discontinuity) for the derivative, but this does not change the fact that the derivative does not exist for $x=\pm1$.
Dec
7
comment Is $|\ln|x||$ differentiable?
@gbox No, you can not use it when the outer function has zero derivative at zero.
Dec
7
comment Is $|\ln|x||$ differentiable?
And this is supposed to solve what exactly? It looks to me like blind and foolish application of the derivative without seeing any details and consequences.
Dec
7
revised Is $|\ln|x||$ differentiable?
Improved formatting. Added +- to the limits.
Dec
7
suggested approved edit on Is $|\ln|x||$ differentiable?
Dec
7
awarded  Nice Answer
Dec
1
comment Easy way of memorizing values of sine, cosine, and tangent
This is a very useful thing. You basicall have to remember that (in radians), if the denominator is $6$ or its divisor, the answer is: half of an integer root. Then it only takes a bit of intution/imagination to recall where on the unit circle the given angle is, and you get the answer!
Nov
19
comment Prove that the equation has exactly n real roots
@SayantanSantra If $x$ a multiple root of a polynomial $P$, it is a root of its derivative. Now it's enough to rewrite the equation as a polynom, and take the derivative.
Nov
17
comment integrate sin(x).
@Hurkyl I know, I commented in this sense in one of the other answers. This is not important; the important thing is that the constants are dependent on each other...
Nov
17
revised integrate sin(x).
improved formatting
Nov
17
answered integrate sin(x).
Nov
17
suggested approved edit on integrate sin(x).
Nov
17
comment integrate sin(x).
@Elll Because two primitive function to any $f$ can differ by a constant. So you prove that $\cos 2x = k+2\cos^2 x$ for one value of $k$. To determine the constant, it is enough to determine it for one point. Plugging in $x=0$, you get $1=k+2$ whence $k=-1$. (This all works if the domain of $f$ is connected, i.e., an interval.)
Nov
15
comment Group Theory: let $G$ be a group and let $G=H\times K$, is it true that $G/H\cong K$?
@Letian kernel = the preimage of the identity element.
Nov
14
comment Normal $(\frac{n-1}{n})$-percentile asymptotic to $(2\log n)^{1/2}$?
Let us continue this discussion in chat.
Nov
14
comment Normal $(\frac{n-1}{n})$-percentile asymptotic to $(2\log n)^{1/2}$?
But in the last displayed equation, you plug $\sqrt{2\log n}$ in the formula, which cannot be done; the fact that $b_n/\sqrt{2\log n}\to1$ does not mean that $f(b_n)$ and $f(\sqrt{2\log n})$ have the same limit, where $f(x)$ is the complicated fraction. You are basically doing a limiting per partes, which works only in some well defined cases.
Nov
14
comment Normal $(\frac{n-1}{n})$-percentile asymptotic to $(2\log n)^{1/2}$?
Well, if such $b_n$ exists, then it is the $b_n$ that solves $P(X>b_n)=1/n$, isn't it?
Nov
14
comment Normal $(\frac{n-1}{n})$-percentile asymptotic to $(2\log n)^{1/2}$?
Isn't it that there exists $b_n$ such that $b_n^2/2\ln n\to1$ and the limit you want is also $1$?
Nov
14
comment Prove that the only $3×3$ matrices which commute with any $3×3$ matrices are of the form $cI$ for some scalar $c$…
@PabloSanchez If $a_{i,i}\neq a_{j,j}$, then $A$ does not commute with the matrix that has all zeros but an element in position $(i,j)$.