Christian Ivicevic
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 Apr 15 comment Calculating exponential limit First of all What have you tried thus far and why do you think you know the result? and furthermore did you mix up $n$ and $x$ variables? What is $x$? Apr 1 comment Simplify $(n+1)^{1/\sqrt{n}}$ and $(n^2+1)^{1/n}$ Yeah I was considering $\sqrt[n]{n}\to 1$ as well but couldn't really compare the sequences to this root. Mar 30 comment Issues computing $\int\cos^2x~\mathrm{d}x$ without using $\sin^2(x)=1-\cos^2(x)$ I know that I am going round and round but I was curious whether there is a more thorough explanation why besides $(\cos x)''=-\cos x$. Mar 29 comment Issues computing $\int\cos^2x~\mathrm{d}x$ without using $\sin^2(x)=1-\cos^2(x)$ @YuriyS Chosing between $\sin x$ and $\sin x$ can yields different results - it the same :P Mar 26 comment Prove the series $\sum_{n=1}^∞ (-1)^n(n)/(n+2)$ diverges @Garrett $$\frac{n}{n+2}=\frac{1}{1+2/n}\overset{n\to\infty}{\longrightarrow}1\neq 0$$ Feb 12 comment Deducing the series expansion of $\arctan(x^2)$ via the series expansion of $\arctan(x)$ at $x=0$ So we must show that the replacement still yields a valid power series and that it has the same radius of convergence? Jan 27 comment Multivariable taylor series expansion of $\exp(-(x^2+y^2))$ Am I right in assuming that $-\exp(-5)(4x+2y-11)$ would be the right polynomial in my case? Jan 21 comment Eigenvectors of $\begin{pmatrix}6&2\\-10&-1\end{pmatrix}$ (linear equations with complex numbers) @Prospect I do know the algorithm but I am struggling with the particular steps in this specific case. Dec 9 comment Continuous function taking each of its values twice It seems I am misunderstanding something in regards to the claim from the paper as all examples that come to mind have a finite amount of discontinuities. Dec 9 comment Continuous function taking each of its values twice Every function that satisfies this property has an infinite number of discontinuities. Refer to ams.org/journals/proc/1986-098-02/S0002-9939-1986-0854049-8/… Dec 9 comment Using L Hopital's Rule Using $e$ $e=\exp(1) \rightarrow (\exp(1))'=(1)'\cdot\exp(1)=0$ as AndreasT mentioned. Dec 8 comment Definite integral $\int _{0}^{1}\sqrt [3] {2x^{3}-3x^{2}-x+1}~\mathrm dx$ What have you tried so far? Dec 7 comment Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$ Could you please elaborate why the term $[-\ln(x)/(\mu x^\mu)|_1^M$ remains finite as $M\to\infty$? Dec 2 comment Trying to understand some terminology Short version: $\mathcal{O}(n)$ is the class of functions which behave asymptotically similiar to $f(n)=n$. You would say that a function is in $\mathcal{O}(n)$ if it does not grow much faster than $n$. Examples would be $2n, 14n,\ldots$. Refer to this article for more detailed information about Big O notation. Dec 1 comment How does one come up with the anti-derivative? In short: Let $F$ be the anti-derivative of $f$ then $F'=f$. Nov 28 comment Give me hints for evaluating this limit If I am not overlooking anything this is true indeed. I guess you just need to explain your reasoning more detailed. Moreover you have to check whether you are allowed to apply my hint - if it is for a homework, then the question is whether you have already proven the hint in a lecture etc. Nov 28 comment Give me hints for evaluating this limit Hint. $e^x=\lim_{n\to\infty}(1+x/n)^n$ Nov 21 comment Reconstructing a function from its critical points and inflection points @kccu Well you can just add a constant to $f$ s.t. $f(x_2)=0$ and it should be $7/7680$ if you work with rajb245's points $x_1,x_2,x_3$ - I am currently experimenting with other numbers for a better scaling but the general idea of this approach is definitely good. Nov 21 comment Reconstructing a function from its critical points and inflection points @whatever Well saddle points are just inflection points with the added property that $f'(x)=0$. I guess there are multiple names that are being used for both types hence the confusion. :) Nov 21 comment Reconstructing a function from its critical points and inflection points @whatever Every saddle point is an inflection point but not the other way round if I am not mistaken. The slope at a saddle is always zero while it does not have to be zero for inflection points.