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 Apr 22 awarded Necromancer Oct 19 comment Why is $\tan^{-1} (\tan(4 \pi/5)) = - \pi/5$ not $4 \pi/5$? Learn something about domain and image of a function. Oct 14 comment Variance of Product of Uniform and Normal Random Variables Find the distribution for Z=XY, and then calculate Var(Z). Oct 12 comment Minimize $5\sqrt{36+x^2}+4(20-x)$ using Lagrange Multipliers My fault, I should have clearly stated it as "equality constraints". Please read the wikipedia page for Lagrange multipliers. And then you'll see, you don't need that in this problem. Oct 12 comment Minimize $5\sqrt{36+x^2}+4(20-x)$ using Lagrange Multipliers Check when to use Lagrange multipliers. You don't have constraints in this problem. Oct 12 comment How should I calculate $\lim_{n\rightarrow \infty} \frac{1^n+2^n+3^n+…+n^n}{n^n}$ Another proof for $e^{k-n} \geq (k/n)^n = e^{n \ln (k/n)}$: $\Leftarrow k-n \geq n \ln (k/n) \Leftarrow \frac{k}{n}-1 \geq \ln \frac{k}{n}$ $\Leftarrow$ for $x>0$, $x-1 \geq \ln x$ $\Leftarrow$ Let $y(x) = x-1-\ln x$, then the stationary point should satisfy $y'=1-\frac{1}{x}=0$; meanwhile $y''=x^{-2}>0$. Thus $y_{\min} = y(1) = 0$, for all $x>0$, $y(x) \geq 0$. Oct 12 comment How should I calculate $\lim_{n\rightarrow \infty} \frac{1^n+2^n+3^n+…+n^n}{n^n}$ @JohnMa Did you? $(1/n)^n$ was substituted with $e^{1-n}$, $(2/n)^n$ with $e^{2-n}$, ..., $(\frac{n-1}{n})^n$ with $e^{n-1-n}$, and $(\frac{n}{n})^n$ with $e^{n-n}$. Oct 12 comment How should I calculate $\lim_{n\rightarrow \infty} \frac{1^n+2^n+3^n+…+n^n}{n^n}$ @JohnMa For every term $(k/n)^n \leq e^{k-n}$, k = 1, 2, ..., n, so it should be "The limit should be no larger than ..."? Oct 10 comment How do you find the Fourier transform of a function? @BLAZE technically, yes. Oct 10 comment How do you find the Fourier transform of a function? @BLAZE if still cannot understand, you can always try the simplest case to help you. Just let $f(x,y)=x+y$, and then calculate $\int f(x,y)\; dx$. Sep 18 comment Assistance with proof of $(AB)^T=B^T A^T$ Check a very simple case, say 1*2 & 2*3, you will find the problem. Sep 17 comment Find equation of circle with reduced radius What's the Radius of the larger circle? Sep 13 revised why is frobenius norm of a matrix greater than or equal to the 2 norm? added 780 characters in body Sep 12 awarded Yearling Dec 20 awarded Constituent Dec 16 awarded Caucus Apr 11 answered Prove that $f(x)=(e^x-1)(x^2+3x-2)+x$ has exactly one positive root, exactly one negative root and one root at $x=0$. Apr 10 comment Prove that $f(x)=(e^x-1)(x^2+3x-2)+x$ has exactly one positive root, exactly one negative root and one root at $x=0$. Solve $f'(x)=e^x (x^2+5x+1) - 2x -2 = 0$, i.e. $e^x (x^2+5x+1) = 2x +2$. Because $e^x$ doesn't change the sign of $x^2+5x+1$, $y=e^x (x^2+5x+1)$ at most has two intersection points with the line $y=2x +2$. Thus $f(x)=0$ at most has three roots, and you have found them all. Apr 10 comment Power calculation for simplification? @RoyiNamir Not quite. But for further information about that, I suggest you read wikipedia pages about IEEE754, "float", and "double". If you have any problem on these issues, it may be better to ask it on stackoverflow.com Apr 10 comment Power calculation for simplification? @RoyiNamir 6.805647*10^38 - 0.000000406*10^38 = (6.805647-0.000000406) * 10^38. Please distinguish "multiplication" and "power" :)