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Having a bit o' fun with math.


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Jun
27
comment Show $\lim_{n_\rightarrow \infty}\int_0^\infty ne^{-\frac{2n^2x^2}{x + 1}}dx = \infty$
(Oops, my comment had a silly mistake.) Your answer quite decisively settles the issue.
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Mar
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comment Limit of the ratio of the logs, knowing the ratio
I'd be surprised if you could say much about the relationship between the two ratios in general.
Mar
28
comment Limit of the ratio of the logs, knowing the ratio
Not necessarily: consider $f(x)=x^a$, $g(x)=x^b$ with $a<b$. Then the first limit is zero but the second limit is again $a/b$ which gives us any positive value $<1$...
Mar
28
comment Limit of the ratio of the logs, knowing the ratio
Suppose $f(x)=x^a$ and $g(x)=x^b$, then if $a>b$ the first limit is $\infty$ but the second limit will be $a/b$ - this we can achieve any positive value for the second limit. If $f(x)=e^x$ and $g(x)=x$ then both limits are $\infty$.
Nov
23
awarded  Yearling
Apr
27
answered Reference for general-topology
Dec
27
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Apr
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comment On the equation $3a^2-4b^3=7^c$
BTW Twh article "Computing integral points on Mordell’s elliptic curves" by Gebel, Petho, Zimmer shows that the torsion groups are trivial (Prop.3.1) and the article may give the tools to complete the proof of the result.
Apr
1
answered A generic question on stochastic integrals
Apr
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answered On the equation $3a^2-4b^3=7^c$
Mar
31
answered Logical reason for the intersection of an infinite family of open sets not being necessarily open
Mar
31
comment On the equation $3a^2-4b^3=7^c$
There are solutions beyond the trivial $(\pm1,-1,1)$, for example $(\pm13,5,1)$, as well as families of solutions --- if $(a,b,c)$ is a solution, then clearly $(a\cdot 7^{3m}, b\cdot 7^{2m}, c+6m)$ is also a solution for $m>0$.