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Jul
18
revised Trigonometric Integrals $\int \frac{1}{1+\sin^2(x)}\mathrm{d}x$ and $\int \frac{1-\tan(x)}{1+\tan(x)} \mathrm{d}x$
deleted 2 characters in body
Jul
18
answered Trigonometric Integrals $\int \frac{1}{1+\sin^2(x)}\mathrm{d}x$ and $\int \frac{1-\tan(x)}{1+\tan(x)} \mathrm{d}x$
Jul
17
comment Show that $\Sigma_{k=1}^{\infty} \frac{\sin kx}{k}$ converges uniformly on any compact subset of $(0,2\pi)$
Recall that $\sin(kx) = \Im (e^{ikx})$
Jul
11
revised $\sum_{i=1}^n\frac{1}{i}\binom{n}{i}p^i(1-p)^{n-i}\leq\frac{K}{n} $
added 56 characters in body
Jul
11
comment $\sum_{i=1}^n\frac{1}{i}\binom{n}{i}p^i(1-p)^{n-i}\leq\frac{K}{n} $
(+1) For neat manipulations!
Jul
11
answered $\sum_{i=1}^n\frac{1}{i}\binom{n}{i}p^i(1-p)^{n-i}\leq\frac{K}{n} $
Jun
23
comment Prove that $\exists k\in \mathbb{N}^*$ such that $\|a-a_k\|<\varepsilon$
ah, you are right! Totally assumed continuity
Jun
23
comment Prove that $\exists k\in \mathbb{N}^*$ such that $\|a-a_k\|<\varepsilon$
Can you prove that f must have a fixed point?
Jun
20
comment Show Covergence, Integral
Well, the argument actually shows quite the opposite. Your integral diverges
Jun
20
comment Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
Use the fact that there is a complex number $z_{0}=e^{it}$ such that $$z_{0}\int_{|z|=1}{f(z) \, dz}= |\int_{|z|=1}{f(z) \, dz}|$$
Jun
20
answered Show Covergence, Integral
Jun
14
comment Sum of two gamma-distributed random variables
Hint: Transformation theorem
Jun
11
revised prove limit with integral is equal supremum
added 62 characters in body
Jun
11
revised prove limit with integral is equal supremum
added 25 characters in body
Jun
11
comment Improper integral: $\int_0^\infty \frac{sin^4x}{x^2}dx$
Hint: $\frac{\sin^{4}(x)}{x^{2}}$ is continuous on $[0,1]$
Jun
11
answered prove limit with integral is equal supremum
Jun
9
answered Infinity norm of continuous function.
Jun
8
comment Topological spaces in which every proper closed subset is compact
Any Disconnected topological space will work just fine. The proof in this particular case is pretty obviuos aswell.
Jun
6
comment If $f_n \to f$ uniformly on compact sets, does $f_n(u) \to f(u)$ in $L^2$ and is $|f_n(u)|$ uniformly bounded?
Since you have a bounded domain, the constants are in $L^{2}(\Omega)$, so DCT is used as usual
May
22
answered integrate $1/(x(x^2-1)^{1/2})$