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visits member for 3 years, 11 months
seen Jul 23 '13 at 15:47

Mar
24
suggested suggested edit on Question regarding positive-definite matrices
Mar
14
revised Regarding orthonormal basis
added 188 characters in body
Mar
14
accepted Regarding orthonormal basis
Mar
13
asked Regarding orthonormal basis
Feb
24
answered Divergence of an improper integral - |cos(x^2)|/x^q
Feb
10
awarded  Citizen Patrol
Feb
9
comment If $f(x)\nearrow\infty$ in $[a, \infty)$ and $f'(x)$ is continuous in $[a, \infty)$ then $\int_{a}^{\infty}\frac{f'(x)}{f(x)}\sin(f(x))$ converges
@Adrian: I think it means $f(x)$ is increasing in the interval and $\lim_{x\to\infty}f(x)=\infty$.
Feb
5
accepted Question regarding Weierstrass M-test
Feb
5
comment Question regarding Weierstrass M-test
@Jonas: if you want to put that down as an answer, I'll gladly accept it.
Feb
5
comment Question regarding Weierstrass M-test
@Jonas: I see, something like $\sum \frac{(-1)^n}{n}$?
Feb
5
comment Question regarding Weierstrass M-test
@Jonas: not sure I follow. What should be constant?
Feb
5
comment Question regarding Weierstrass M-test
Thanks. One question though: why is $\sup_{x\in I} |u_n(x)| \geq u_n(n) = 1/n$?
Feb
5
comment Question regarding Weierstrass M-test
@Jonas: interesting. Will $\log(1+x)=\sum (-1)^{n+1}\frac{x^n}{n}$ work? Here $I=(-1, 1]$ and at $x=1$ we'll get $\frac{1}{n}$.
Feb
5
asked Question regarding Weierstrass M-test
Feb
4
comment How to know that $a^3+b^3 = (a+b)(a^2-ab+b^2)$
I love how simple, yet very helpful your explanations are.
Feb
3
accepted Show $\int_{0}^{\infty}\sin(f(x))dx$ converges if $\int_{0}^{\infty}f(x)dx$ converges and $f(x)$ is a decreasing, continuous function in $[0, \infty)$
Feb
3
comment Show $\int_{0}^{\infty}\sin(f(x))dx$ converges if $\int_{0}^{\infty}f(x)dx$ converges and $f(x)$ is a decreasing, continuous function in $[0, \infty)$
@Steven: could you give a hint as to why $f(x)\to 0$? I understand why intuitively but having some difficulty showing it... I'm familiar with a similar result that had $\lim_{x\to \infty}f(x)$ existed, then $\lim_{x\to \infty}f(x)=0$ must be true.
Feb
3
comment Show $\int_{0}^{\infty}\sin(f(x))dx$ converges if $\int_{0}^{\infty}f(x)dx$ converges and $f(x)$ is a decreasing, continuous function in $[0, \infty)$
@Joe: not sure I follow. You're saying $\int_0^\infty f(x) dx \implies \lim_{x\to \infty}f(x)=0$? What about $g(x)=x$ if $x \in N,\ g(x)=0$ otherwise?
Feb
3
comment Show $\int_{0}^{\infty}\sin(f(x))dx$ converges if $\int_{0}^{\infty}f(x)dx$ converges and $f(x)$ is a decreasing, continuous function in $[0, \infty)$
@Arturo: Why does $f(x)\to 0^+$?
Feb
3
asked Show $\int_{0}^{\infty}\sin(f(x))dx$ converges if $\int_{0}^{\infty}f(x)dx$ converges and $f(x)$ is a decreasing, continuous function in $[0, \infty)$