Christian Ivicevic
Reputation
1,245
Top tag
Next privilege 2,000 Rep.
 Dec 8 revised Definite integral $\int _{0}^{1}\sqrt [3] {2x^{3}-3x^{2}-x+1}~\mathrm dx$ Improved formatting. 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 8 suggested approved edit on Definite integral $\int _{0}^{1}\sqrt [3] {2x^{3}-3x^{2}-x+1}~\mathrm dx$ 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 7 asked Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$ Dec 4 revised Convergence of $\sum_{n=1}^{\infty}f(n)$ $\iff$ convergence of $\int_1^{\infty}$f(x)dx added 25 characters in body Dec 4 answered Convergence of $\sum_{n=1}^{\infty}f(n)$ $\iff$ convergence of $\int_1^{\infty}$f(x)dx Dec 3 revised Testing series for convergence Exchanged the image of the formula with MathJax Dec 3 suggested approved edit on Testing series for convergence 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 $F'=f$. Dec 1 revised How the tackle this limited integral? Changed the images with proper MathJax formulas Dec 1 suggested approved edit on How the tackle this limited integral? Nov 28 answered Give me hints for evaluating this limit 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 27 accepted Throwing the dice - wrong interpretation still yields correct result Nov 27 asked Throwing the dice - wrong interpretation still yields correct result Nov 22 accepted Reconstructing a function from its critical points and inflection points 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.