Tab Content
• Today, 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 | 76 view(s) • Today, 09:14 It's like this: $$\Big(1-\frac 12 x^2 + \ldots\Big)\Big(1+\frac 12 (2x)^2 - \ldots\Big)\\ =1\cdot 1 -\frac 12 x^2 \cdot 1+1\cdot \frac 12 (2x)^2 -... 7 replies | 76 view(s) • Today, 07:04 The series expansion of \cos x = 1 - \frac 12x^2 + \ldots. And the expansion of \frac 1{1-x} = 1+x+x^2+\ldots So:$$\frac{\cos(x)}{\cos(2x)}... 7 replies | 76 view(s) • Today, 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 | 33 view(s) • Today, 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 | 128 view(s) • Yesterday, 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 | 55 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 | 158 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 | 158 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 | 144 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 | 125 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 | 144 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 | 404 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 | 404 view(s) • March 30th, 2020, 04:26 Yep. (Nod) And no, nothing more specific. 21 replies | 404 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 | 404 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 | 404 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 | 404 view(s) • March 29th, 2020, 14:38 Indeed. (Thinking) 21 replies | 404 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 | 404 view(s) • March 29th, 2020, 14:26 Yep. (Nod) 21 replies | 404 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 | 404 view(s) • March 29th, 2020, 13:57 Then the inequality also holds yes. What if fill in, say,$f'(y)=-1$in the inequality? Would it satisfy it? (Wondering) 21 replies | 404 view(s) • March 29th, 2020, 13:52 mathmari replied to a thread Limits & properties in Analysis Ah$(-\infty)\cdot (+\infty)$is also an undefined form, isn't it? So$f'(y)$is either$0$or$-\infty$, right? (Wondering) 21 replies | 404 view(s) • March 29th, 2020, 13:19 That is a possibility yes. What happens if$f'(y)$is negative? (Wondering) 21 replies | 404 view(s) • March 29th, 2020, 13:14 mathmari replied to a thread Limits & properties in Analysis So that we get that$\ell$is not infinity we have to get an undefined form, one such form is when infinity is multiplied with zero, so$f'(y)$must... 21 replies | 404 view(s) • March 29th, 2020, 13:08 We have an expression with$f(y)$,$f'(y)$, and$\ell$. And we already know that$\ell\in\mathbb R$, don't we? So it can't be$\pm\infty\$ either. ...
21 replies | 404 view(s)
• March 29th, 2020, 12:28
mathmari replied to a thread Limits & properties in Analysis
So we have the following: \begin{align*}f(x)\geq f(y)+f'(y)(x-y)&\Rightarrow \lim_{x\rightarrow +\infty}f(x)\geq \lim_{x\rightarrow...
21 replies | 404 view(s)
• March 29th, 2020, 10:27
Ah okay. But that is not the case now is it? (Wondering) Sounds like a plan. (Nod)
21 replies | 404 view(s)
More Activity

### 57 Visitor Messages

1. Hey Rido, Happy Birthday! How've you been?
2. Happy Birthday, Rido!
3. *rido
oops lol
4. Thanks ride hope everything is good for you too
5. Happy Birthday Rido12! I wish you another healthy year with loads of fun, excitement, beautiful memories and all your wishes & dreams come true!
6. Happy bday Rido12! I hope you're having a great time.
7. Happy Birthday, Rido12!!!
8. wb when you get the chance
9. you never clear you inbox i left something for you on the wb
10. hey . check wb.
Showing Visitor Messages 1 to 10 of 57
Page 1 of 6 123 ... Last
Page 1 of 6 123 ... Last

#### Basic Information

Date of Birth
June 23
Biography:
Student and Musician. Passionate about mathematics and physics.
Country Flag:

#### Statistics

Total Posts
714
Posts Per Day
0.29
Thanks Given
3,441
847
1.186
##### Visitor Messages
Total Messages
57
Most Recent Message
June 23rd, 2018 19:49
##### General Information
Last Activity
March 2nd, 2020 15:02
Last Visit
March 1st, 2020 at 16:43
Last Post
January 11th, 2019 at 02:47
Join Date
July 18th, 2013
Referrals
3
Referred Members
bobthefairycat, justinc, KingofDerp

### 20 Friends

MHB Master

2. #### BacteriusOffline

MHB Journeyman

MHB Master

4. #### Chris L T521Offline

MHB Journeyman

MHB Master

MHB Master

MHB Master

Perseverance

9. #### Henry ROffline

MHB Apprentice

10. #### ineedhelpnowOffline

MHB Journeyman

Showing Friends 1 to 10 of 20
Page 1 of 2 12 Last