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• Today, 01:06
No one answered to POTW #409. Here is a suggested solution from other: The function S(x)=\sum_{k=1}^{70}\dfrac{k}{x-k} is discontinuous at...
2 replies | 243 view(s)
• April 6th, 2020, 17:02
Prove It is not giving you the answer he is giving you a suggestion that you can use the limit he posted. See if there is any kind of substitution...
6 replies | 107 view(s)
• April 6th, 2020, 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 $x$...
4 replies | 74 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 | 243 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 | 187 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 | 250 view(s)
• April 2nd, 2020, 11:56
topsquark replied to a thread f in Calculus
I believe the proper question is "What the 'f'?" -Dan
5 replies | 360 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 | 349 view(s)
• March 31st, 2020, 17:53
topsquark replied to a thread [SOLVED] 299What is the acceleration in Calculus
Wait! What do you mean by you changed it to v(t)? The particle's position is x(t) = sin(t) - cos(t) means that v = \dfrac{dx}{dt}. You can't just...
4 replies | 351 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 | 349 view(s)
• March 27th, 2020, 23:42
Here is this week's POTW: ----- Find the minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\dfrac{9}{v}\right)^2$ for $0<u<\sqrt{2}$ and $v>0$. ...
1 replies | 187 view(s)
• March 27th, 2020, 23:38
Hi MHB! I have decided to extend the deadline by another week so that our members can give this problem another shot and I am looking forward to...
2 replies | 243 view(s)
• March 26th, 2020, 20:42
Have you tried looking at \lim_{n \to \infty} \dfrac{a_{n + 1}}{a_n}? -Dan
2 replies | 114 view(s)
• March 26th, 2020, 18:35
Let y'(x) = v(x). Then your equation becomes v'(x) + v(x) = -F(x) Now you have a first degree linear ordinary differential equation. You can't...
1 replies | 105 view(s)
• March 20th, 2020, 19:44
topsquark replied to a thread [SOLVED] s8.2.5.7 chain rule in Calculus
Look at your first factor: \left ( 7x^6 + 8 x^3 \right ) ^3 = ( x^3 ( 7 x^3 + 8 ) )^3 = (x^3)^3 (7 x^3 + 8 )^3 Don't worry. It's an easy mistake...
2 replies | 314 view(s)
• March 20th, 2020, 02:18
Here is this week's POTW: ----- Show that the set of real numbers $x$ which satisfy the inequality \sum_{k=1}^{70}\dfrac{k}{x-k}\ge...
2 replies | 243 view(s)
• March 20th, 2020, 02:15
Congratulations to the following members for their correct solution! 1. castor28 2. lfdahl 3. kaliprasad 4. Oxide Solution from Oxide: ...
1 replies | 239 view(s)
• March 14th, 2020, 23:06
All of the other answers could be true but since f(x) is not given we could make the function do some or all of these possibilities, as well as...
7 replies | 251 view(s)
• March 14th, 2020, 19:06
I'm just saying that f(x) can be anything so I had fun sketching it. -Dan
7 replies | 251 view(s)
• March 14th, 2020, 19:04
Just to round out the thread I (finally) have an explanation of 3) from my original post. (It looks worse than it is.) p^{ \mu } p^{ \nu } \to ...
7 replies | 733 view(s)
• March 14th, 2020, 17:50
Since we aren't given any real information about f(x) we need to be general. It's possible that f(x) can be just about anywhere is this interval. ...
7 replies | 251 view(s)
• March 14th, 2020, 10:49
The key to this lies in Theorem 1.3.5, which says that $x\in\overline{A} \Longleftrightarrow U\cap A\ne\emptyset$ for every (open) nbd of $x$. ...
2 replies | 98 view(s)
• March 14th, 2020, 10:01
This follows from the statement immediately before Proposition 1.3.2, where it says that $A$ is open if and only if $A = A^\circ$. Since $A^\circ$ is...
1 replies | 64 view(s)
• March 13th, 2020, 10:03
Here is this week's POTW: ----- How many perfect squares are divisors of the product $1!\cdot 2! \cdot 3! \cdots 9!$? ----- Remember to...
1 replies | 239 view(s)
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### 6 Visitor Messages

1. Hi lfdahl,

Thanks for the kind words! But you know, this posting of challenge problems stuff, it is always a two-way street, so, I also want to thank you for attempting and posting your solutions to some of my challenge problems before and last but not least, I sure hope to see your participation in my future challenges!

Best wishes,

anemone
2. Hi lfdahl,

It looks like your account here has exceeded its stored private messages quota and cannot accept new message(s). Unless you clear some space, I can in no way to reply to your PM.

Anyway, I wanted to tell you I appreciate all the kind words that you sent to me in the PM and I hope to seeing you more around at our forum.

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anemone
3. You are welcome! Glad you are here.
4. Hi Ifdahl! Although it's a bit late, I want to warmly welcome you to MHB. Hope you enjoy the time spent here.
5. Hello and welcome to MHB, Ifdahl!

If you have any questions or comments about the forums, please feel free to address them to me or another staff member. We are happy to help and look forward to your participation here!

Best Regards,

Mark.
6. Hi lfdahl,

Welcome to MHB! We encourage you to begin asking or posting here to make use of the forum!
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#### March 17th, 2020

• 21:09 - anemone clicked Thanks for this post: -= Hidden Content =- by lfdahl

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Name: MHB Challenges Award (2017)
 Issue time: February 11th, 2018 21:19 Issue reason:

Name: Secondary School/High School POTW (2014)
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