Math Challenge - October 2018

In summary: Calculate the following limit: $$ \lim_{x\to 1} \frac{x}{x^2+1}$$ (by @Math_QED )In summary, summer is ending and fall is beginning, which means it's time for a change. The monthly math challenge questions have been combined into one thread, and there are still several open problems from last month. Some of the problems are on a high school level, and those should be left for high school students to solve for at least two weeks. The problems include solving a Lagrangian differential equation, determining a sigma-algebra, calculating integrals, finding the area enclosed by a curve, and solving limits.
  • #71
fresh_42 said:
The entire thing is positive, continuous and bounded, so Fubini applies.
^This.
That is what I should have answered to the Q: "Justify the initial equality by which theorem?" Except for at the origin, a singlet of measure zero. But that the integrand was unbounded thereat seemed to justify a little caution on my part; that and not knowing which Fubini Theorem variant to use. But then you both are experts, @fresh_42 strikes me as a seasoned Analysis prof, or the equivalent in terms of wit.
 
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  • #72
@fresh_42 added 7. e) to post #63 (done)
 

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