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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.
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.
Nov
21
revised Reconstructing a function from its critical points and inflection points
added 151 characters in body