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Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
I just clicked "edit" and then "roll back" on the first revision, if that's what you're asking.
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
I rolled the question back to what it was originally. You should probably add a disclaimer to your answer so people don't start downvoting you.
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
Also, what sort of course are you following that you can talk about minimal surfaces but don't know the derivative of $x^2+x$?
Oct
25
comment Suppose $S$ is a minimal surface, show that the gaussian curvative is negative on all interior points
Please don't change your question to something else. If you have a new question, ask a new question.
Oct
15
comment What's the integral of $\frac{-4x}{1+2x}$?
Constants don't matter when doing integrals. In this case, the $-1$ gets absorbed into the $+C$ that you should have put when doing the integral.
Oct
14
comment How do we explain to students that division by a vector does not make sense?
It certainly depends on what your multiplication is.
Oct
9
comment Is there a elementary way to prove $\zeta(2)=\frac{\pi^2}{6}$
The top answer in that post is as elementary as it gets, considering we ate dealing with infinite series. You're not likely to find anything simpler.
Oct
6
comment How to tell if multivariable function is odd?
You just do. It's something you get used to after a while. After all, it's usually pretty easy to tell at a glance whether a function is odd.
Oct
5
comment Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f $.
Are those powers or derivatives?
Sep
30
comment Why do we think of a vector as being the same as a differential operator?
I think I like your answer the most, but I'll wait a bit longer just in case another one pops up. Thanks!
Sep
29
comment Why do we think of a vector as being the same as a differential operator?
Why is it the only sensible definition? If I have a point $p \in M$ and an open set $U \ni p$ with local coordinates $\phi: U \to \mathbb{R}^n$, then I can choose (for example) the standard basis of $\mathbb{R}^n$, and if I want to use another coordinate system, the vectors transform as dictated by the Jacobian, so my basis is well-defined regardless of the coordinates. Isn't this right?
Sep
28
comment is it true that $\det(I+A)>0$ , if $\det(A)>0$?
+1 This is the simplest example, I think.
Sep
26
comment How to show that the is a $1-1$ correspondence between real numbers and the set of points of a line in the Euclidean plane?
I think the question is about the relationship between $\mathbb{R}$ as a set of numbers and the geometric notion of a line, but I could be wrong.
Sep
25
comment Why do we think of a vector as being the same as a differential operator?
@GeorgesElencwajg: If you think that's the answer, then post it as so. But I still wonder: if there's no reason to make no distinction, why does the author make no distinction?
Sep
22
comment Simplify the expression.
Isn't this needlessly complicated? Why not just substract exponents at the second equality, if you're going to do it later anyway?
Sep
21
comment Integrating $\sec^2 x$ from first principles
Why would you not know that? It's not magic, it's very easy to derive.
Sep
21
comment lim calculus problem with infinity
@vilbur: $\frac{n+5-2}{n+5} = \frac{(n+5)-2}{n+5} = \frac{n+5}{n+5} - \frac{2}{n+5} = 1-\frac2{n+5}$.
Sep
21
comment lim calculus problem with infinity
Also, the nth-root of n goes to $1$. If you don't believe me, take the logarithm of the expression.
Sep
21
comment lim calculus problem with infinity
The fraction goes to $1$ but the exponent goes to $\infty$; this doesn't go to $1$ but rather is an indeterminate case, as evidenced by the well known fact that $(1+\frac1{n})^n \to e$.
Sep
18
comment Does infinite time = time with no end = never?
The short answer is that if it takes an infinite amount of time to reach point B, then the object never reaches it. Of course, in the real world, no matter how precise your measurement is, there will be some time after which the object is closer to B than your instrument can distinguish.