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 Dec 19 awarded Constituent Dec 9 awarded Caucus Nov 16 comment Single formula for this sequence 1/4 ((-1)^n + (-1)^(2 n)) n. Don't ask if it is not related to Mathematica programming. Sep 24 awarded Autobiographer Aug 31 comment Approximate the largest and the smallest values of the integral Since the integrand is positive in the given range {1, 3} the smallest value is at $1$ and the largest value is at $3$. Approximate values are NIntegrate[t/Sqrt[2 + t^3], {t, -1, #}] & /@ {1, 3} i.e. {-0.0764949, 1.15208}. Apr 5 comment Behaviour of a function in differential equation Is it anyhow related to Mathematica (a computer system) programming? Jan 4 comment Solving: How to find an inverse function for this function? Defining y[x_] := 2 + Log[Sqrt[x] - 1] you get the answer with InverseFunction[y], e.g. InverseFunction[y][2] yields 4. You don't have to care about the warning when you work with real numbers x > 1. Oct 28 comment How to factorize an equation? possible duplicate of Factoring polynomials to factors involving complex coefficients Sep 18 comment Taylor series problem @Stefano From this equation: -55.20 + 6598.80 i - 30794.40i^2 == 0. Solution i = 0.205566 is just an artefact of approximation by a Taylor series. For a bit of Mathematica code see the answer by belisarius. Sep 18 comment Taylor series problem @DanielLichtblau You can check these steps are correct until the last line, the result should be i == 0.00872 || i == 0.205566 it is different by a factor 10. Nevertheless approximate solution i == 0.00872 is correct, it just shouldn't be i == 0.00753. Jun 6 comment How to plot this problem? From Greek Exams @lafkasd If you've asked this question consider registering your account and merge it with user7851. It hasn't been obvious if this question regarded Mathematica programming or you just plotting certain mathematical object (so how to plot it ?). Therefore they have sent it here. Jun 3 answered How to plot this problem? From Greek Exams Jun 3 comment How to plot this problem? From Greek Exams What do you mean by the curve v^3+a2*v^2+a1*v+a0 = 0 ? To plot all the three curves (three roots of the equation depending on a0, a1, a2)? If so then it should be a three-dimensional submanifold, not just one-parameter curve. May 17 awarded Constituent May 6 awarded Caucus Mar 16 comment How to evaluate $I=\displaystyle\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$ @robjohn I believe it might be proved symbolically in Mathematica. I'll check if it can be done. By the way I'm Artes not Aries. Dec 29 awarded Yearling Nov 20 comment Finding the 2,147,483,647th prime number @DanNeely In reference.wolfram.com/mathematica/tutorial/… you can find e.g. a note on Number Theoretic Functions, it says Prime and PrimePi use sparse caching and sieving. For large n, the Lagarias-Miller-Odlyzko algorithm for PrimePi is used, based on asymptotic estimates of the density of primes, and is inverted to give Prime.  Nov 19 comment Finding the 2,147,483,647th prime number @awashburn You can compute Prime[2147483647] in Wolfram|Alpha as well, since it relies on Mathematica. Nov 19 comment Finding the 2,147,483,647th prime number The approximation of $\pi(x)$ is good asymptotically (prime number theorem) but for any finite number it may be far from the correct value which is 50685770143 for 2147483647 th prime. A better approximation is given by the Riemann prime counting function.