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### confusing limits

calculate this limit when x tend to infinity : f(x) = (x+5)^(1+1/x) - x^(1+1/x+5) I used Laurent series at infinity but in the middle I confuesd and can not solve it but I am sure the correct answer ...
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### Manifestation of Hecke operator on the category of abelian varieties (or motives)

If we are given some postivie integer $N$ and a prime $p$, then we have the Hecke operator $T_p$ on modular forms, which is a cohomological manifestation of the Hecke correspondence X_0(N)\leftarrow ...
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Suppose $(X, G, \Omega, \mu)$ is a dynamical system where $(X, \Omega, \mu)$ is a Borel measure space and $G$ is acting on $X$ such that each group action $x\mapsto g\cdot x$ defines a measurable ...