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• Today, 15:25
It's a "rite of passage" for calculus students. (Smile)
3 replies | 22 view(s)
• Today, 12:48
Right. So what that means is that there is no angle $\alpha$ that specifically has $\sin\alpha=\frac 1n$ (rational) and also a rational...
8 replies | 109 view(s)
• Today, 12:03
Those two answers only differ by a constant, because $\cot^2 x+ 1 = \csc^2x$.
3 replies | 22 view(s)
• Today, 12:01
Clear, thank you. I think my texts are too introductory to come across this notation.
5 replies | 87 view(s)
• Today, 11:48
It holds for $\alpha=\arctan(3/4)$ because $(3,4,5)$ is a Pythagorean triple. The point is that there is no such triple having $1$ as one of its...
8 replies | 109 view(s)
• Today, 09:04
By that logic that would hold for any angle, wouldn't it? But it doesn't, since with $\alpha=\arctan(3/4)$ both $\cos\alpha$ and $\sin\alpha$ are...
8 replies | 109 view(s)
• Today, 08:58
Not quite that simple! What that argument shows is that $\sin10^\circ$ and $\cos10^\circ$ cannot both be rational. In that case, there would indeed...
8 replies | 109 view(s)
• Today, 07:20
l will now attempt to, explicitly, complete the demonstration that Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) ...
4 replies | 62 view(s)
• Today, 04:56
Let $x = \sin10^\circ$. The formula for $\sin3\theta$ shows that $3x - 4x^3 = \sin30^\circ = \frac12.$ So $8x^3 - 6x + 1 = 0.$ If $y=2x$ then $y^3 -... 8 replies | 109 view(s) • Today, 04:29 Yep. (Nod) 12 replies | 173 view(s) • Today, 02:23 Hi, Peter. Try dividing the first line of (2.11) through by$t$. Now take the limit as$t\rightarrow 0$, use the definition of directional... 1 replies | 40 view(s) • Today, 01:11 Here is an attempt to show Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) Now we have ... Df(a) v =... 4 replies | 62 view(s) • Today, 00:59 Thanks Country Boy ... ... appreciate the help ... Peter 4 replies | 62 view(s) • Today, 00:54 Thanks GJA ... that was really helpful ... Still reflecting on what you have said ... Thanks again ... Peter 2 replies | 60 view(s) • Yesterday, 23:26 Here is this week's POTW: Let$ABCD$be a convex quadrilateral with$\overline{AB}=\overline{AD}$. Let$T$be a point on the diagonal... 0 replies | 34 view(s) • Yesterday, 23:21 No one answered this weeks POTW...my solution follows: (a) Apply conservation of angular momentum (subscripts of$R$pertain to the rod, while... 2 replies | 149 view(s) • Yesterday, 18:27 Conceptually an integral corresponds to the area under a graph. If that graph extends to infinity, the height of the graph must approach zero, since... 12 replies | 173 view(s) • Yesterday, 18:06 Erm... then I'm not quite sure what I can use or not. Can you perhaps use the fact that a series$x_1 + x_2 + ...$can only converge if$x_n \to 0$?... 12 replies | 173 view(s) • Yesterday, 17:39 What is the regular/basic definition of limits that you are familiar with? The generic definition is the so-called$\varepsilon$-$\delta$... 12 replies | 173 view(s) • Yesterday, 16:37 The multiplicative inverse of q with respect to q'. That is, it is such that: $$_{q'}^{-1} \cdot q \equiv 1 \pmod {q'}$$ And since$q$and$q'$... 5 replies | 87 view(s) • Yesterday, 16:31 Thank you, both, very helpful. However, what does$_{q'}^{-1}$mean? 5 replies | 87 view(s) • Yesterday, 16:10 Suppose$\lim\limits_{x\to\infty} f(x)=c > 0$. Then for$\varepsilon = \frac c 2 > 0$there must be some$a$such that for every$x>a$we have that... 12 replies | 173 view(s) • Yesterday, 15:58 Hi, Peter. This question is perhaps a little deeper than it seems initially. The subtlety lies in the fact that$\phi_{a}(x)$is an... 2 replies | 60 view(s) • Yesterday, 15:36 Hey MermaidWonders! Let's start with$\int_0^{\infty} f(x)\,dx$, which must also converge. Then$\lim\limits_{{x}\to{\infty}}f(x) = 0$isn't it?... 12 replies | 173 view(s) • Yesterday, 15:23 Hi steenis, Suppose$\gcd(m,m')=d$, then we can write$m=qd$and$m'=q'd$with$\gcd(q,q')=1$. And suppose$b\equiv b' \pmod d$, so that... 5 replies | 87 view(s) • Yesterday, 15:09 Hi, steenis. Start with two solutions, say$x$and$y$, to the system. We want to show that$l$divides$x-y$. Since$x$and$y$solve the system... 5 replies | 87 view(s) • Yesterday, 11:12 Let$m$and$m'$be positive integers, and$d=gcm(m,m')$. (i) The system:$x \equiv b (mod \ m)x \equiv b' (mod \ m')\$ has a solution if...
5 replies | 87 view(s)
• Yesterday, 07:38
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
4 replies | 62 view(s)
• Yesterday, 06:50
I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2:...
1 replies | 40 view(s)
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### 18 Visitor Messages

1. Sometimes editing a thread title is an issue, but the issue is with vBulletin. If you ever want to change a thread title, and can't, just let me know and I can fix it.
2. Hey Peter!

I edited your post to remove the duplicate content. Sorry for the late reply, I was busy "powering through" a tedious 3 hour project.
3. Glad to hear that resolved the issue! I thought perhaps forcing your browser to reload the script by removing it from your cache might do the trick.
5. Hey Peter,

No, there have been no changes in that regard, at least that I know of. Do you visit any other sites that use MathJax? If so does it render there?

Best Regards,

Mark.
6. Good deal, Peter! I wish I had a nickel for every time a problem is corrected by ditching IE and using a modern standards compliant browser.
7. I would try another browser...IE is notorious for being problematic.
8. Hello Peter,

No changes to composing posts have been made. What browser are you using? What OS?
9. Thank you for your kind words Peter, I really appreciate them. I'm always happy to help!
10. Hey Peter,

You attached 4 images, but only 3 of them were attached inline...I deleted the duplicate.

Best Regards,

Mark.
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#### February 17th, 2018

• 19:49 - Peter clicked Thanks for this post: -= Hidden Content =- by skeeter

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