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Jan
22
comment Subgroup of $\mathbb{Q}$ containing $\mathbb{Z}$
Do you take group w.r.t. to $+$ or $\times$?
Jan
22
comment How can you find $m$ in $mx^2+(m-3)x+1=0 $ so that there is only one solution
I don't think so and I give you +1; this approach is slightly different than in the other answers and shows a nice use of Vièta's formulas.
Jan
22
comment Calculating $\lim_{n\to\infty}\sqrt[n]{ \sqrt[n]{n} - 1 }$
No, the OP did not do that, but it's easy, because $n^{1/n}>1$ for all $n$.
Jan
10
comment When does one consider the laplacian as a dirac delta function?
The direct calculation does not work at zero (the origin), which is where you're losing your delta function. It's similar to saying that the derivative of $x\mapsto|x|$ is the signum of $x$; you lose one point.
Jan
10
comment How many sequences of rational numbers converging to 1 are there?
Isn't simply $\mathbb{N}^\mathbb{N}$ a continuum, whence also $\mathbb{Q}^\mathbb{N}$ is?
Dec
27
comment How can one determinate the variationt of $f(g(x))$
@user233658 Because $f$ is decreasing for arguments $<1$ and increasing for arguments $>1$.
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
mickep @Ian Oh I now realize the trick (sorry it's early in the morning here). That looks really nice, thanks!
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
@Ian Yes, I know. The problem is that this is for 1st year university students, and we tend to disallow using derivatives for limits at the beginning. And after one does what you do, it gets very complicated. Thanks for your help anyway!
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
@Ian If you ever write $y'$, you are quite obviously using derivatives.
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
@Ian How do you prove convexity?
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
I have exactly the problem @sranthrop speaks about. How do you prove that $e^t\geq t+1$ without taking derivatives?
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
As $\lim (1+x/n)^n$, I'll include this.
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
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
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.