• Today, 11:02
To follow up, we can use the derivative to find the time rate of change of the angular displacement, which is typically denoted by $\omega$. ...
2 replies | 45 view(s)
• Yesterday, 06:59
Hello and welcome to MHB! (Wave) We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions....
2 replies | 45 view(s)
• Yesterday, 02:52
Thanks GJA ... Appreciate your help ... Peter
3 replies | 48 view(s)
• Yesterday, 01:55
MarkFL replied to a thread Domain...2 in Pre-Calculus
No factor in the denominator can be zero, and nothing under a square root radical can be negative...so this leads to: t-1\ne0 0<t What do...
1 replies | 28 view(s)
• Yesterday, 01:47
I would write: y=\frac{2x}{x-1}=\frac{2x-2+2}{x-1}=\frac{2(x-1)+2}{x-1}=2+\frac{2}{x-1} We see this will have a horizontal asymptote at $y=2$,...
1 replies | 30 view(s)
• Yesterday, 01:31
Let's look at a definition: |u|=\begin{cases}u, & 0\le u \\ -u, & u<0 \\ \end{cases} Can you see that we must have: 0\le|u| ?
2 replies | 48 view(s)
• March 19th, 2018, 22:43
I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations:...
3 replies | 48 view(s)
• March 19th, 2018, 22:30
Yes, and as Wilmer was pointing out, you would likely want to use the binomial theorem. If you raise both sides to the 5th power, you get: ...
10 replies | 107 view(s)
• March 19th, 2018, 21:56
You're being asked to find an area, and in essence, you're doing so by adding up a bunch of vertical lines, the length of which are determined by the...
5 replies | 54 view(s)
• March 19th, 2018, 21:48
To follow up, we get: \d{x}{t}=\frac{\d{y}{t}\left(x-12y^2\right)}{9x^2-y} Plugging in the given values, we find: ...
4 replies | 52 view(s)
• March 19th, 2018, 21:07
That's already included in the "top curve minus the bottom curve." :)
5 replies | 54 view(s)
• March 19th, 2018, 18:56
Yepper! Get well soon...
7 replies | 77 view(s)
• March 19th, 2018, 17:37
Well, your 375,462.29 result is way off: should be 176,900.08 Calculation (i = .0425/12): 704.26* / i = 176900.08 Then you need the future value...
7 replies | 77 view(s)
• March 19th, 2018, 15:10
Will do; pleasure is all mine. All yours Mark...
10 replies | 107 view(s)
• March 19th, 2018, 14:12
Didn't "introduce" anything... YOU asked about raising to 5th power... Gave you an example. HOKAY?!
10 replies | 107 view(s)
• March 19th, 2018, 13:15
SIMPLE: total payments - amount borrowed You knew that...right??
7 replies | 77 view(s)
• March 19th, 2018, 13:08
Well, you'd have quite a few terms to manipulate; as example: (a + b)^5 = a^5 + 5 a^4 b + 10 a^3 b^2 + 10 a^2 b^3 + 5 a b^4 + b^5
10 replies | 107 view(s)
• March 19th, 2018, 12:54
So that results in M = 9.12 You can tell right away that's not correct. So why lose your time and ask? Regarding this sentence in problem:...
6 replies | 72 view(s)
• March 19th, 2018, 09:46
Let's first look at the bounded region: And so the area is: A=\int_0^3 (-x^2+6x)-(x^2-2x)\,dx=2\int_0^3 -x^2+4x\,dx=2\left_0^3=2(18-9)=18 ...
5 replies | 54 view(s)
• March 19th, 2018, 08:38
To follow up, the washer method gives us: V=\pi\int_{x_1}^{x^2} R^2-r^2\,dx The volume of an arbitrary washer is: ...
3 replies | 83 view(s)
• March 19th, 2018, 04:16
Thanks castor28 ... Hmm ... beginning to understand what you are saying ... Still concerned and a bit confused ... Surely R/I is a ring...
6 replies | 65 view(s)
• March 19th, 2018, 03:53
Thanks for the help, castor28 ... But just a point of clarification ... You write: " ... ... The identity of $R/I_1$ is $I_1$ ... ... " ...
6 replies | 65 view(s)
• March 19th, 2018, 02:24
I would first observe that $1+\sqrt{5}$ is a root of: x^2-2x-4=0 And so, the coefficients of the expansion: (1+\sqrt{5})^n Can be found...
10 replies | 107 view(s)
• March 19th, 2018, 02:16
I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations:...
6 replies | 65 view(s)
• March 19th, 2018, 02:02
2 replies | 36 view(s)
• March 19th, 2018, 02:00
2 replies | 43 view(s)
• March 18th, 2018, 23:25
1 replies | 106 view(s)
More Activity

### 72 Visitor Messages

1. Hey Balarka, according the the settings in the ACP it is 5 minutes.
2. Hey Balarka, Daniel is upgrading the forum software to a completely new platform. It should be back up soon.
3. I agree that fun shouldn't introduce wrong concepts.

PS: Yes, I'll add one when I start the next post.
4. Ok, then you are looking at rigor but as I said these tutorials will be for fun. I want a high school student to understand it. It would be great to have your comments when I start posting bout that, though. I know I can learn from you as I am haven't read that much about these concepts.
5. What is your definition of Regularization ?
6. We can extend the zeta function to analytic function in the whole complex plane except at 1. By definition we have
$$\zeta(s) =\sum \frac{1}{n^s}$$
So zeta on the left is analytic for all $s \neq 1$ but the sum on the right does only converge for $Re(s) >1$.
So the analytic continuation of zeta has enabled us to give values to the divergent sum on the right.
7. Hey Balarka , the idea of regularization is giving a finite value for divergent series or integrals. Consider the following
$$\zeta(-2)= 0$$
$$1+4+9+\cdots = 0$$
8. Okay, thanks. I think the former one is just what I wanted.
9. Hey Balarka, I do not know of a closed for that sum. But there are some identities related to this problem:
\begin{align*} \sum_{k=1}^p \frac{H_k^{(2)}}{k}+\sum_{k=1}^p \frac{H_k}{k^2} &= H_p^{(3)}+H_p^{(2)}H_p \\ \sum_{k=1}^p \frac{H_k^{(2)}}{k}+\sum_{k=1}^p \frac{(H_k)^2}{k} &= \frac{(H_p)^3+3H_p H_p^{(2)}+2H_p^{(3)}}{3} \end{align*}
To prove these, we can use induction.
10. Possibly, that's my name there. I don't gravitate toward your usual tags, I suppose. I'm more in multivariable calculus, calculus and lower level ones.
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#### Basic Information

Date of Birth
January 12, 2000 (18)
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
Location:
West Bengal, India
Interests:
Number Theory
Country Flag:
India

#### Signature

Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

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