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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
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Jun
11
revised prove limit with integral is equal supremum
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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 $1/(x(x^2-1)^{1/2})$
May
22
comment use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
I think it suffies to compute the fourier coefficients of $\sin^{2}(x)$ if you insist of using Parseval
May
19
comment Prove that a finite union of closed sets is also closed (using limit points)
The easiest way of proving your statement is in my opinion is by using the fact that a subset $F$ of a set $X$ is closed iff $X-F$ is open. Then applying De Morgans Law your problem reduces to proving that a finite intersection of open subsets is open, which is a definition in general topological spaces.
May
19
answered Simple Congruence Problem
May
11
comment Prove/disprove space is complete with metric defined by an integral (triangle inequality still missing in metric part)
To show that $f_{n}$ is a cauchy sequence the only interval to consider is indeed the middle one in our case. You can just calculate it explicitely since it is only a difference between two powers of x and let m,n tend to infinity. Next is to show that this sequence cannot converge to a continuous function on (-1,1)
May
10
answered Prove/disprove space is complete with metric defined by an integral (triangle inequality still missing in metric part)
May
10
revised How to compute this multivariable limit?
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