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• Users: longrob
• In Calculus
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1. ### To show that an integral is divergent

Thanks for your reply. That's what i thought. So I assume the easiest/typical way is the way I described above ?
2. ### To show that an integral is divergent

Hi all I am looking for a simple way to show that the mean of the Cauchy distribution us undefined. This is because this integral diverges: \underset{-\infty}{\overset{\infty}{\int}}\frac{x}{x^{2}+a^{2}}dx Now, I know one proof which replaces the limits of integration with -x1 and x2. After...
3. ### Obvious integral manipulation

This wasn't obvious to me. From my book. We have, p(x)=\begin{cases} \frac{1}{2} & -2\leq x\leq-1\,\textrm{or}\;1\leq x\leq2,\\ 0 & \text{otherwise~}.\end{cases} So, the kth moment is given by M_{k}=\frac{1}{2}\int_{-2}^{-1}x^{k}dx+\frac{1}{2}\int_{1}^{2}x^{k}dx So, obviously...

Thanks !
5. ### Weibull integral

Can someone explain this.. P(v)=\frac{\beta}{\eta}\intop_{0}^{v}\left(\frac{v}{\eta}\right)^{\beta-1}\exp\left(-\left(\frac{v}{\eta}\right)^{\beta}\right)dv=\intop_{0}^{x}e^{-x}dx\hphantom{}\; where\phantom{\:}x=\left(\frac{v}{\eta}\right)^{\beta} Thanks !
6. ### What's this function ?

Perfect. Thank you.
7. ### What's this function ?

Thanks. I considered arctan already, but since this function goes momentarily vertical zero arctan doesn't work. Same with a Gompertz function and Richards curve (I think). Also, this function appears to be odd, so that would rule out a Gompterz function also. Are there Sigmoid curves that are...
8. ### What's this function ?

Thanks, but I've not been able to find one. Any suggestions ?
9. ### What's this function ?

Hi all What are some candidate functions f(x) that satisfy these conditions: 1. domain of f is R 2. image of f is (-1,1) 2. Smooth and continuous everywhere 3. first derivative undefined at x=0 4. f(x)-->1 as x--> inf 5. f(x)-->-1 as x--> -inf Thanks LR