Emanuele Paolini
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 Mar 3 comment How to prove the following formula is a constant? what if you change variable in the integrals and let $x=\rho y$? Jan 11 comment Showing that if a function is $O(x^2)$, then it's also $o(x)$ For $x \to a\neq 0$ you have $O(x^2) = O(1)$ and $o(x) = o(1)$. And yes, they are different. Jan 7 comment Showing that if a function is $O(x^2)$, then it's also $o(x)$ Whatever is $C$ one has that $C|x|\to 0$ as $x\to 0$. Jan 7 comment A positive measurable and improper integrable function is integrable yes, it is correct. Jan 7 comment A positive measurable and improper integrable function is integrable We can but not have to. Jan 7 comment Rational and irrational numbers under base pi I don't know. But here en.wikipedia.org/wiki/Non-integer_representation you find some references. Dec 29 comment What is the value of $\frac{\sin x}x$ at $x=0$? I would not say that $f$ is not continuous at $x=0$. Continuity is only defined for points of the domain. Dec 20 comment Evaluate $\lim\limits_{x\to\infty}x(\frac{\pi}{2}-\arctan(x))$ without using L'Hôpital Do you know that $\sin(t) / t \to 1$ as $t\to 0$? Dec 20 comment Wind vector transformation from Gaussian grid to displaced pole grid Could you provide the formula used to transform points? Dec 15 comment Maximum Probability to hit the bear. It's not clear from the problem statement if the hunter knows when the bullets hits the bear. Dec 6 comment Differentiating $e^x$ from first principles using limits. You should specify which is the definition of $e^x$. The answer can vary. Dec 4 comment Are $A^c$ and $B^c$ homeomorphic? More interesting: if $A$ and $B$ are compact, connected and homeomorphic. Are the complementary sets homeomorphic? Nov 25 comment Continuous inclusions in locally convex spaces Now I understand. I think the procedure is correct. Nov 25 comment What is the probability that he counts head more that tails when tosses a coin 6 times right... corrected! Nov 25 comment What is the probability that he counts head more that tails when tosses a coin 6 times I added the conclusion... Nov 23 comment Prove limit superior of a sequence is greater than or equal to limit superior of the Cesàro mean of that sequence Your proof cannot work, because if $x_n$ is decreasing you always have $(\sum_{i=0}^n x_n)/n > x^*$... Nov 17 comment Given an elementary set how to obtain an open elementary set containing it whose measure is less than a desired quantity If you have a finite union of open intervals, if the intervals have intersection you can join them to obtain a disjoin union of open intervals. Nov 17 comment A Matrix $A$ that $A^2$ is not I, but $A^4 = I$ What about rotations? Nov 11 comment Is $\gamma$ homotopic to $g\circ\gamma$? I suppose that a simply connected space is also connected. In that case you can join the two starting and ending points with a continuous curve. Hence you assign the value of the homotopy $F$ on the boundary of $I\times I$. The function can then be extended on the interior by the definition of simply connectedness. If, instead, a simply connected space is not required to be connected, the statement is obviously false. Nov 8 comment Change of variables problem. You want to plot the image of what? Please try to write a clear question.