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5h
comment How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
(+1) that works, too.
7h
comment How can I obtain this division's limit without using derivatives?
@user246608: $\lim\limits_{x\to0}\frac{\sin(x)}x=1$ is derived geometrically in this answer.
10h
revised Show that this difference goes to zero,
add the error estimate for the Riemann Sum
10h
comment Show that this difference goes to zero,
Ah, I forgot to include the approximation error. I will add that.
11h
revised How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
improve exposition
11h
answered How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
12h
answered Show that this difference goes to zero,
12h
revised How to take into account uncertainty on number of events
approximate the expected value of $\frac1n$ when $n$ has a Poisson distribution.
17h
comment How to take into account uncertainty on number of events
I think I misunderstood the question previous to the last edit. I now believe that your question is asking for the variance of $\frac1n\sum\limits_{k=1}^nX_k$. Is that correct? I have amended my answer to cover this case, too.
17h
revised How to take into account uncertainty on number of events
answer the question that I think was asked
21h
answered How to take into account uncertainty on number of events
1d
revised the best constant in an inequality?
drop the variational method for a basic Cauchy-Schwarz approach
1d
revised the best constant in an inequality?
Use the equality in Cauchy-Schwarz
1d
revised the best constant in an inequality?
give an alternate approach
1d
revised the best constant in an inequality?
the sum is equal to this
1d
answered the best constant in an inequality?
1d
comment Evaluate $\displaystyle\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^\frac{1}{n} \ \mathrm{d}x$
(+1) However, on $\left[\frac12,1\right]$, note that $\left[1+\left(\frac{1-x}x\right)^n\right]^{1/n}\le2$ and easily $\lim\limits_{n\to\infty}\left[1+\left(\frac{1-x}x\right)^n\right]^{1/n}=1$. From these observations alone, we can apply Dominated Convergence.
1d
comment Combinatorics Question - Permutations and Supersets
It would be, but it is more precise than that, we have $$n!e-\frac1n\le\lfloor n!e\rfloor\le n!e$$
1d
answered Combinatorics Question - Permutations and Supersets
1d
revised Find a constant $C$ such that $ \Bigg| \frac{\prod_{i=0}^{k-1} (n-i) }{n^k} - 1 \Bigg| \leq \frac{C}{n}, \forall k \leq n$
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