• Today, 17:57
When I throw it at Octave online, I get: So it seems it is none of the above, but the answer $3$ is close. For reference, I have re-encoded...
1 replies | 30 view(s)
• Yesterday, 12:06
Hi all, I think even we do switch to XF (is still going to happen) the time has come to make a change. We have a database of amazing content here...
1 replies | 108 view(s)
• Yesterday, 11:37
Hi all, I hope you are all safe, healthy, and not affected in a serious way by the world wide COVID-19 virus. Here in the US it has completely...
0 replies | 47 view(s)
• Yesterday, 11:34
Hey mathmari!! This is an example where Newton-Raphson can have problems if we are not careful. If we pick a starting value that is too far from...
2 replies | 41 view(s)
• Yesterday, 10:30
\frac{\left(x\sin\left(\pi\left(x-1\right)\right)\right)}{e^{x/9}(x-1)} The above graph shows that the function repeats its value at $x=1$ when $x$...
2 replies | 41 view(s)
• Yesterday, 08:49
Hey!! :o The function \begin{equation*}f(x)=\frac{x}{e^{x/9}}\cdot \frac{\sin \left (\pi (x-1)\right )}{x-1}\end{equation*} has at exactly one...
2 replies | 41 view(s)
• April 5th, 2020, 10:37
I substituted $n=\frac 1{x^2}$, which also means that $x^2=\frac 1 n$. So we get $\Big(1 + \frac 32 x^2\Big)^{1/x^2} = \Big(1 + \frac 32 \cdot \frac... 7 replies | 232 view(s) • April 5th, 2020, 09:14 It's like this: $$\Big(1-\frac 12 x^2 + \ldots\Big)\Big(1+\frac 12 (2x)^2 - \ldots\Big)\\ =1\cdot 1 -\frac 12 x^2 \cdot 1+1\cdot \frac 12 (2x)^2 -... 7 replies | 232 view(s) • April 5th, 2020, 07:04 The series expansion of \cos x = 1 - \frac 12x^2 + \ldots. And the expansion of \frac 1{1-x} = 1+x+x^2+\ldots So:$$\frac{\cos(x)}{\cos(2x)}... 7 replies | 232 view(s) • April 5th, 2020, 01:08 Here is this week's POTW: ----- Suppose that the positive integers$x, y$satisfy$2x^2+x=3y^2+y$. Show that$x-y, 2x+2y+1, 3x+3y+1$are all... 0 replies | 180 view(s) • April 5th, 2020, 01:02 No one answered last week's POTW.(Sadface) Below is a suggested solution: The given function is the square of the distance between a point of the... 1 replies | 147 view(s) • April 4th, 2020, 04:14 This is actually a proof of (ii)$\Rightarrow$(iii) in Lemma 3.2. So we are assuming that (ii) holds. In particular, since$\overline{ f(A) }$is... 1 replies | 194 view(s) • April 3rd, 2020, 22:31 I am reading Aisling McCluskey and Brian McMaster: Undergraduate Topology, Oxford University Press, 2014... ... and am currently focused on Chapter... 1 replies | 194 view(s) • April 2nd, 2020, 12:25 Klaas van Aarsen replied to a thread f in Calculus It appears the answer is: dkm Acronym for "don't kill me". Often used when somebody says something that somebody else finds really funny,... 5 replies | 303 view(s) • April 1st, 2020, 06:35 Not quite, although you started correctly. The limit in this case is as$x\to\infty$, so you want to see what happens when$x$gets large. This means... 3 replies | 282 view(s) • March 31st, 2020, 14:52 Hi Goody, and welcome to MHB! To prove that \lim_{x\to\infty}\frac{x-1}{x+2} = 1, you have to show that, given$\varepsilon > 0$, you can find$N$... 3 replies | 282 view(s) • March 30th, 2020, 05:31 Let's take a look at a couple of examples. If$f(x)=x$, then$f'(x)=1$and$f''(x)=0$. So$\lim\limits_{x\to +\infty}f'(x)\ne 0$, isn't it?... 21 replies | 470 view(s) • March 30th, 2020, 04:35 mathmari replied to a thread Limits & properties in Analysis Ok!! As for the second question, why is the limit always zero? (Wondering) 21 replies | 470 view(s) • March 30th, 2020, 04:26 Yep. (Nod) And no, nothing more specific. 21 replies | 470 view(s) • March 30th, 2020, 03:57 mathmari replied to a thread Limits & properties in Analysis OK, so it's graph is a decreasing function, right? Or can we say something more specifically? (Wondering) 21 replies | 470 view(s) • March 30th, 2020, 03:32 I believe so yes. Consider$f(x)=\ell$. It satisfies all conditions, doesn't it? (Wondering) And it is monotone instead of strictly monotone. To... 21 replies | 470 view(s) • March 29th, 2020, 17:21 mathmari replied to a thread Limits & properties in Analysis I don't see how we get the strict inequality. Is maybe the result wrong and it should be monotone instead of strictly monotone? (Wondering) 21 replies | 470 view(s) • March 29th, 2020, 14:38 Indeed. (Thinking) 21 replies | 470 view(s) • March 29th, 2020, 14:31 mathmari replied to a thread Limits & properties in Analysis Ok! That means that$f$is monotone and escpecially descreasing, right? To get that$f$is strictly monotone, do we have to get$f'(x)<0$instead of... 21 replies | 470 view(s) • March 29th, 2020, 14:26 Yep. (Nod) 21 replies | 470 view(s) • March 29th, 2020, 14:18 mathmari replied to a thread Limits & properties in Analysis Yes, because then from$\ell\geq f(y)+f'(y)(+\infty-y)$we get$-\infty$at the right side of the inequality, and so$\ell$can be real. ... 21 replies | 470 view(s) More Activity ### 33 Visitor Messages 1. hey can u help me plz 2. Testing$\LaTeX$embedded within text...$ \displaystyle \int_a^b f'(x)\,dx=f(b)-f(a)\$...
3. Lol took it down cuz I'm not active. Is that a request to get it back up? Lol
4. Hey ILS. Think you could check my quantum physics question? Thanks!
5. Thanks
6. Hey ILS. I think you got your fraction inverted in this post.
7. Congratulations on topping the 3,000 post mark...3,000 quality posts I might add. Well done!
8. "That's because I'm having a bad day."

How that happens to everyone of us!
9. ILS, can you please give me further assistance on the snails thread? Please let me know which part of my working is unclear, I will try my best to explain it.

Thanks!
10. Congratulations, I like Serena! You have hit the 2k posts today, and out of the 2k posts, I said all of them are the most helpful and informative ones!
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