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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?
added 138 characters in body
May
10
answered How to compute this multivariable limit?
Mar
28
comment Evaluate a limit using integral
I thought that the limit was $$\lim_{n\rightarrow \infty}\lim_{x\rightarrow 1 -} \sum_{k=1}^{2n}\frac{(-x)^{k-1}}{k}$$ I think the real issue here lies in the fact that we actually can interchange the limits in your suggested way, but how does one motivate such a step?
Jan
30
answered multivariable limit problem
Jan
27
revised Integral $\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \ln(1+c\sin x) dx$, where $0<c<1$
deleted 185 characters in body
Jan
27
answered Integral $\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \ln(1+c\sin x) dx$, where $0<c<1$
Jan
20
comment Prove $\int_{0}^{1} |\frac {f^{''}(x)}{f(x)}| dx \geq 4$
What about $f(x)=x(x-1)$ isn't that a counterexample?
Dec
30
awarded  Curious
Dec
29
asked Evaluating a sum $-\zeta'(2)$
Dec
24
comment A not complete metric space?
We know that $\mathbb{R}$ with the usual metric $d(x,y) =|x-y|$ is a complete metric space. Since the exponential function is continuous, then we usually would expect the $|e^{x}-e^{y}|$ should be small aswell... But maybe it has something to so with uniformness..
Dec
24
comment A not complete metric space?
Is your statement even true?
Dec
10
accepted Ideal in a ring of continuous functions
Dec
9
awarded  Caucus
Nov
26
answered Fourier Transform of $\exp(-t)$