Zarrax
Reputation
28,128
356/400 score
 17h comment Matrices where A^2 = A This aint exactly rocket science here :) 2d revised If $\vec p\times((\vec x-\vec q)\times\vec p)+\vec q\times((\vec x-\vec r)\times\vec q)+\vec r\times((\vec x-\vec p)\times\vec r)=0$, find $\vec x$ added 1 character in body 2d answered If $\vec p\times((\vec x-\vec q)\times\vec p)+\vec q\times((\vec x-\vec r)\times\vec q)+\vec r\times((\vec x-\vec p)\times\vec r)=0$, find $\vec x$ Apr16 awarded Enlightened Apr16 awarded Nice Answer Apr12 answered Showing that $\int_0^\infty \frac{|\cos x|}{1+x} \, dx$ diverges (Baby Rudin Exercise 6.9) Apr12 answered If p and q are prime which elements are in the subgroup? (GRE question) Apr12 comment Is every open cover of $\{(x,y) \in \mathbb R^2 : x^2+y^2=1\}$ also an open cover of some $\delta$ annulus around the unit circle? If such a positive $\delta$ exists, then if $|w| = 1$ and $z' \notin \cup_{\alpha} U_{\alpha}$, then $|w - z'| \geq \delta$. If $1 - \delta < |z| < 1 + \delta$, then the distance from $z$ to $w = {z \over |z|}$ is less than $\delta$. Hence $d(z',z) \geq d( z', {z \over |z|}) - d({z \over |z|}, z) > \delta - \delta = 0$. This is true for any $z' \notin \cup_{\alpha} U_{\alpha}$, so $z$ must be in $\cup_{\alpha} U_{\alpha}$. Apr12 answered Is every open cover of $\{(x,y) \in \mathbb R^2 : x^2+y^2=1\}$ also an open cover of some $\delta$ annulus around the unit circle? Apr12 answered Compute $\iiint_V \sin^2 (x + y + z) \,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}x$ where $V$ is an ellipsoid. Mar24 answered $\int_{\mathbb R}|f(x)|^{2} dx <\infty \implies \sum_{m\in \mathbb Z}\int_{m-\beta}^{m+\beta}|f(x)|^{2} dx <\infty$? Mar2 answered Prove $\frac{a}c = \frac{a-b}{b-c}$ Feb27 answered Can wolframAlpha be wrong on this vector limit? Feb25 answered Help understanding the proof of Morera's Theorem Feb21 comment If $f:\mathbb{R} \to \mathbb{R}$ has two derivatives such that $f(0) =0$ and $f'(x) \leq f(x), \forall x,$ then $f\equiv 0 \ ?$ Yep, that works. Any function of the form $e^x h(x)$ with $h(x)$ decreasing and $h(0) = 0$ will also work. Feb21 answered Does $\lim_{x \to 0} \frac{\sin (\left \lfloor x \right \rfloor)}{\left \lfloor x \right \rfloor}$ exist? Feb21 answered The value of $\int _{0}^{1}x^{99}(1-x)^{100}dx$ is Feb21 comment If $f:\mathbb{R} \to \mathbb{R}$ has two derivatives such that $f(0) =0$ and $f'(x) \leq f(x), \forall x,$ then $f\equiv 0 \ ?$ $f(x)$ doesn't have to be identically zero... try writing a function satisfying the condition which is not identically zero, there are many. Feb21 comment If $f:\mathbb{R} \to \mathbb{R}$ has two derivatives such that $f(0) =0$ and $f'(x) \leq f(x), \forall x,$ then $f\equiv 0 \ ?$ no idea.. maybe the asker had a different method in mind Feb21 answered If $f:\mathbb{R} \to \mathbb{R}$ has two derivatives such that $f(0) =0$ and $f'(x) \leq f(x), \forall x,$ then $f\equiv 0 \ ?$