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 Mar 24 comment Solving a system of equations with 3 variables in under a minute @egreg I don't buy this your point. To me, the question is formulated in such a way that the equation has some solution. The asker has $x$, $y$ and $z$ in his head and only shares that they satisfy the three equalities. This means that the problem has at least one solution, and then the method in Carl's answer works. Feb 12 answered What number comes next in the sequence $7, 16, 8, 27, 9,…$? 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 revised Number of Perfect Powers in Pascal`s Triangle edited tags 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? Jan 10 answered How many sequences of rational numbers converging to 1 are there? 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 26 revised How can one determinate the variationt of $f(g(x))$ edited tags Dec 26 answered How can one determinate the variationt of $f(g(x))$ Dec 16 accepted Limit of $e^x/x^3$ at infinity without l'Hopital 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 revised Limit of $e^x/x^3$ at infinity without l'Hopital added 54 characters in body Dec 16 comment Limit of $e^x/x^3$ at infinity without l'Hopital As $\lim (1+x/n)^n$, I'll include this.