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10h
comment How do I calculate $ \int_{-\infty}^{\infty} e^{-ax^2} \;\mathrm{d}x$ for $a>0 $
this is a famous integral with no anti-derivative representable in terms of special functions, you could probably just google it
May
11
comment How can I evaluate the following limit-integral combination?
@abiessu, no it doesn't, plus taking the limit of the dummy variable wouldn't make sense anyways.
May
11
comment How can I evaluate the following limit-integral combination?
@abiessu, it's x, I checked it numerically.
May
4
comment Find a basis and the dimension of the eigenspaces of the matrix
This is a symmetric matrix, hence its eigenspace has dimension 3 and you can just choose the standard basis for $\mathbb{R}^3$, no need to find the eigenvectors.
Apr
22
comment Diagonal decomposition, square root and eigenvector / eigenvalue of a matrix
assuming this matrix is even diagonalizable, to get $V$ and $D$ you need to already know the eigenvalues and eigenvectors, or you could just find $V$ and $D$ using computational software, otherwise I would suggest doing $Det(\lambda I - A)$ and seeing if you can factor the cubic.
Mar
31
comment What is the $x$-intercept for $\frac{2x^2}{x^2-1} = 0$
no, I'm referring to multiplying both sides by the denominator of the fraction $x^2 + 1$
Mar
31
comment What is the $x$-intercept for $\frac{2x^2}{x^2-1} = 0$
clearing denominators is a common theme in algebraic simplification
Mar
31
comment What is the $x$-intercept for $\frac{2x^2}{x^2-1} = 0$
because you can just multiply both sides by the denominator and it disappears.
Mar
31
comment What is the $x$-intercept for $\frac{2x^2}{x^2-1} = 0$
what you have in your title is the equation you need to solve to find the x-intercepts, so just solve that equation, and you'll have them.
Jan
3
comment Function on convex set is convex if all rays are convex
skeptical that it's true?
Jan
3
comment Function on convex set is convex if all rays are convex
I know you can't for a general domain $D$, but if we assume that $D$ is open and convex I was wondering if you could.
Apr
9
comment Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$
@ Pedro Tamaroff: I remember those times fondly when you pooped on my chest =)
Apr
8
comment Using the Residue Theorem for a contour integral along the Riemann sphere
I'm busy nuttin', and she still suckin'
Mar
30
comment Limit of infinite loops of sin x as n tends to infinity
Maybe use the fact that for $x\neq0$, $|\sin(x)|<|x|$. Also that $\sin(x)$ is strictly monotonically increasing on $[-1,1]$.
Mar
11
comment Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.
you're right I mis-typed it, I'll fix.
Mar
11
comment Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.
damn that's slick.
Jan
29
comment Prove this matrix is invertible for $n < m-1$
awesome answer, thanks.
Nov
3
comment Singularities in (Elementary) Real Algebraic Geometry
The cubic is $y^3+2y^2+y+(v-u^2)=0$, the roots will be $functions$ of $u$ and $v$, that's what I'm after, so that I can prove that $f(x,y)=(u(x,y),v(x,y))=(x,x^2-(y+1)^3+(y+1)^2)$ has an inverse which is analytic.
Nov
3
comment Singularities in (Elementary) Real Algebraic Geometry
I'm having trouble understanding. Solving $v=f(u,y)$ for $y$ will give me 3 roots, each a function of $u$ and $v$, I should expect that one of these roots is a real analytic function in a nbhd of $(0,0)$, correct?
Oct
5
comment Prove that $\frac{d}{dx}\int_0^xf(x,y)dy = f(x,x)+\int_0^x\frac{\partial}{\partial x}f(x,y)dy$
super slick! =o