Mathematics - 2014-09-25 (page 3 of 5)

Khallil

5:03 PM

If you ding that password, @Nick, you better let me know.

I've been trying to crack it for a while.

Has anybody noticed the updated pinging system?

Über kawaii.

Vibhav Pant

Let $f(x) = (x-a)(x-b)^3(x-c)^5(x-d)^7, a,b,c,d \in \mathbb{R}$. How many distinct roots does $f'(x)$ have?

By Rolle's Theorem it should be having 3 roots, but the answer is 6, any idea?

Khallil

Can it be done simply, @Vibhav?

Will Hunting

I have awoken from my nap.

Khallil

I'm thinking of factorising $(x-b)^2 (x-c)^4 (x-d)^6$ from $f'(x)$.

Cool beans, @Will.

Will Hunting

@Khallil I noticed too.

Vibhav Pant

5:08 PM

@Khallil that gives 3 roots too

Khallil

What about the contents of the stuff you haven't factorised?

$f'(x) = (x-b)^2 (x-c)^4 (x-d)^6 ( \text{extra blah terms that might give another root} )$

Vibhav Pant

@Khallil Wouldnt appying Rolle's Theorem on $f$ (since it is continous everywhere) be easier?

(on $[a,b], [b,c], [c,d]$, but then it gives 3 roots only)

Also, $f'(x) = (x-b)^2(x-c)^4(x-d)^6[(x-b)(x-c)(x-d) + 3(x-a)(x-c)(x-d) + 5(x-a)(x-b)(x-d)+7(x-a)(x-b)(x-c)]$

damn

Khallil

I don't recall the specifics of that theorem, @Vibhav. T_T

Vibhav Pant

@Khallil If $f$ is continuous and differentiable on $[a,b]$ and $(a,b)$ respectively, and $f(a) = f(b)$, then there exists at least 1 $c$ such that $f(c) = 0$

Khallil

What about $f$ being equal to a constant?

@Vibhav?

Vibhav Pant

5:19 PM

Well, then $f'(x)$ will always be zero

(derivative of a constant)

Alizter

@VibhavPant you meant $f'(c)=0$ not $f(c)=0$

Vibhav Pant

oh

never saw that

Now I cant even edit it ;_;

Khallil

Yea, but there won't be exist a $c$ given all of your conditions above, unless the constant equals 0.

Wait, edit what?

-_-

Anywho, it doesn't seem easier to apply that theorem, @Vib.

Vibhav Pant

@Khallil make that $f'(c) = 0$, not $f(c) = 0$

Khallil

Oh.

Vibhav Pant

5:22 PM

So you can apply it on $[a,b], [b,c], [c,d]$ since $f(a) = f(b) = f(c) = 0$

Khallil

Ugh, it just seems so troublesome.

There should be a nice way of dealing with the stuff in the final set of parentheses.

Will Hunting

Has anyone else watched If I stay?

This chat seems a bit quiet today.

Khallil

Who are the star actors/actresses from the movie, @Will?

Will Hunting

@Khallil Nobody I know of. But it is good.

Khallil

As good as ... Good @WillHunting?

Will Hunting

5:30 PM

@Khallil Yes, very good.

Khallil

Is it as good as 'A Beautiful Mind', @Will?

Will Hunting

I will go drink some coffee.

@Khallil Also very good.

Khallil

I meant, is it is good as 'A Beautiful Mind', @Will. Sorry for the ambiguity.

Will Hunting

@Khallil The three all have full marks from me.

Khallil

Oh, it must be very good. I'll try and find some time to see it.

^_^

The Game

5:42 PM

Hello, jellyfishes

Khallil

Deep sea greetings, @TheGame.

The Game

@Khallil Is that a selfie ?

Khallil

Nope, it's a seafie. Birds take skyfies and humans take selfies. There's a big difference, @TheGame.

The Game

@Khallil But you're a jellyfish, not a bird

Khallil

(I feel like writing @Hippa, every time I reply to one of your messages. T_T)

I know. It's a seafie, @TheGame.

Not a skyfie, a seafie. ^_^

Maybe aquafie would be a more appropriate word.

The Game

5:51 PM

If you want i can give you an aquafee

Khallil

I'm good. Can you evaluate this integral, @TheGame?

The Game

What one -__-

Khallil

$$ \displaystyle \begin{aligned} \int_{0}^{\frac{\pi}{2}} \dfrac{1}{1+\tan^{\alpha}x} \text{ d}x \end{aligned} $$

Chris's sis

@Khallil with pen and paper or without pen and paper? :-)

The Game

@Khallil Oh that's complex

Litterally

$\mathbb{C}$

Even for $\alpha=1$

Khallil

6:00 PM

I can assure you that the result isn't complex, @Hippa.

The Game

It is

Khallil

By tapping into Ramanujan's residual spirit, @Chris'ssis. ^_^

The Game

For $\alpha=1$ it is $\frac{\pi}{4} + \frac{i \pi}{2}$

Khallil

Woah. I only got $\frac{\pi}{4}$. :O

The Game

for $\alpha=1$ the indefinite integral is $\frac{x}{2} + \frac{1}{2} \log{\left (\tan{\left (x \right )} + 1 \right )} - \frac{1}{4} \log{\left (\tan^{2}{\left (x \right )} + 1 \right )}$

Khallil

6:02 PM

Should I show you my working out, @TheGame?

The Game

Sure

Khallil

I'd really like to know where you got the imaginary part from. That's really the only way I know how to find that integral.

The Game

Owait I made an error xD

It's indeed $\pi/4$

Khallil

Ah, cool!

Will Hunting

I am bored, lol.

The Game

6:07 PM

@WillHunting Do something

@WillHunting Answer my two last questions

Will Hunting

@TheGame I am only a banana.

The Game

@WillHunting And so ?

►

I should stop, that might draw @sarah here

Will Hunting

Hehe, where is Sarah? LOL.

You guys really love posting pics huh?

Will Hunting

6:35 PM

@Khallil She is quite pretty.

Balarka Sen

@TheGame Google [Lion's Mane Jellyfish]

The Game

@BalarkaSen Hair + Jelly = xqgdfqghdnsd

sarah

I was summoned.

Alizter

@BalarkaSen

A 12 year old asked me this today

@BalarkaSen forget it

I just realised I forgot an extra condition

I will need to consult him again

sarah

6:51 PM

u so silleh

Khallil

Sarah Michelle Gellar is kinda ugly now, @WillHunting.

Sarah Michelle Gellar

Sarah Michelle Prinze (née Gellar; born April 14, 1977) is an American actress and producer. In 1983, she made her acting debut in the made-for-TV movie An Invasion of Privacy and went on to appear in Spenser: For Hire and Crossbow. Gellar had her first lead part in 1992's mini-series Swans Crossing and originated the role of Kendall Hart on the ABC daytime soap opera All My Children, winning the 1995 Daytime Emmy Award for Outstanding Younger Actress in a Drama Series. Gellar came to prominence in the late 1990s, landing roles in 1997's horror films I Know What You Did Last Summer and Scream 2...

sarah

@Khallil I believe the correct term is old. But sooner or later we will all be as "old" as her.

The Game

I'll stay young forever :D

Sawarnik

@Khallil Hey.

Oh @TheGame hey.

The Game

7:09 PM

@Sawarnik Hey

Khallil

►

Sawarnik

I m not gonna watch that.

@Khallil Tomorrow I'll get the results of Semester-I :| English went bad, really bad :(

Khallil

It's the Budweiser 'Wasaaap!' commercial.

How badly, @Sawarnik?

Your English seems perfectly fine here. It doesn't seem like Engrish at all.

I'm sure it went better than you thought!

Buy your teacher a cake or something. English is subjective and I'm sure your teacher can ... change his/her opinion. =P

Sawarnik

Nah, I wrote a crap story, and the literature was bad as well.

@Khallil Yeah, and probably take the cake and reduce my marks :D

Will Hunting

@sarah Here I come, lol.

Khallil

7:17 PM

Don't be afraid, @sarah. You'll be ugly too. =P

(Don't take that seriously.)

((It was all in good fun.))

Will Hunting

@Khallil Some people stay pretty forever, like Mariah Carey, lol.

Khallil

That's because of the most recent advancements in make-up, @WillHunting.

Sawarnik

You know very well Khallil, how come?

Khallil

How do you know that I know very well, @Sawarnik?

^_^

Sawarnik

@Khallil You seem to.

:P

Khallil

7:20 PM

Well played. Tips fedora

Will Hunting

I just emailed Living Language to find out if their Complete Edition takes me to B2 or other levels in the CEFR.

Khallil

You can just tell that some people wear loads of maquillage when you see them in natural light, @Sawarnik.

Sawarnik

What is a maquillage? Hmm.

Khallil

I guess it's more common where I live, however.

Will Hunting

I am now watching youtube.com/watch?v=-U0JdnNp1gI.

Sawarnik

7:22 PM

So true, quora.com/…

(removed)

@Khallil How many girls are before you (or the other way round)?

Khallil

What do you mean by before me, @Sawarnik?

sarah

@WillHunting

Will Hunting

@sarah I am here.

sarah

@WillHunting this is a favorite

Will Hunting

@sarah I am listening now. I like the picture, lol.

sarah

7:27 PM

@WillHunting The music is so beautiful I didn't realise the picture

:P

Alizter

ergh

Chemistry.SE is horrible

Will Hunting

@sarah Both are beautiful, like you.

Khallil

Smooth, @Will.

Smooth.

sarah

@WillHunting Why thank you? However i could be an evil green witch.

hehehheheeeee

Khallil

Or a 60 year old man.

:O

Sawarnik

7:29 PM

lol

sarah

I hate that word

Will Hunting

I think it is cauldron.

Alizter

@sarah is 60

Will Hunting

@sarah Did you check out the link I gave you yesterday?

sarah

@WillHunting it be broken

arggh

Will Hunting

7:29 PM

@sarah Really? It worked for me.

Alizter

a 60 year old pirate

Sawarnik

pirate?

sarah

@WillHunting oh, there was a comma after the link

its fine now

Khallil

Are you good at maths, @sarah?

Will Hunting

@sarah Hehe, that is our secret, shh...

sarah

7:31 PM

@WillHunting you look a bit grey

;)

@Khallil nobody is good at math

Khallil

I beg to differ.

sarah

just some people are better

@Khallil You look like you are setting up for a question? Go ahead. Questionate.

Sawarnik

@Khallil Are you good [at math]?

Khallil

Yea. I'm good.

I'm doing well.

How are you, @Sawarnik?

I wasn't setting anything up, @sarah.

Alizter

@Khallil you gooded well

sarah

7:33 PM

@Khallil oh. No questions? :(

Will Hunting

@sarah Have you finally watched The covenant? LOL

sarah

@WillHunting I have not had time. Too much study.

Hence why I am here ;)

Will Hunting

@sarah OK, but the movie I watched last week is really good: If I stay.

Khallil

You're studying here, @sarah? o_O

I dun goofed, @Alizter. I dun goofed.

sarah

@Khallil there is a book on my laptop if that is what you are saying.

Khallil

7:35 PM

Nope, that wasn't what I was saying.

Sawarnik

Bye.

@Khallil :)

Khallil

Until our paths cross again, @Sawarnik. ^_^

Alizter

@Khallil I dropped D2

doing D1 again

sarah

@Khallil you like D2?

puns away from bad joke

Khallil

Do you know what D2 is, @sarah?

puns away ...

-_-

sarah

7:38 PM

no, but I read it as dick 2. You know. The abreviation

hahahahaha

I should study

Will Hunting

I thought it meant D cup, lol.

sarah

@Alizter is a d cup

Will Hunting

@sarah What are you studying now?

sarah

@WillHunting math

Will Hunting

@sarah What topic?

sarah

7:39 PM

^_^

Balarka Sen

@Alizter WAT

Alizter

@BalarkaSen read further up

you know what I should delete that

Khallil

@sarah @WillHunting

sarah

@WillHunting I am starting probability distributions

Will Hunting

@sarah OK. Remember, this chat will waste your time, so don't come here anymore. =)

Alizter

7:41 PM

@sarah you probably are

sarah

@WillHunting i don't need to go to school till monday. I am good

Will Hunting

@sarah I miss my undergrad days. So carefree...

Clash

Hi, could anyone tell me what's an m-diagonal matrix is? Is this being both an M matrix and a diagonal matrix?

Alizter

@Clash yup

Khallil

Isn't there a band called The Clash?

sarah

7:42 PM

m m m m matrix

Will Hunting

M for math. M for mum. M for money.

Daniel Fischer

@Khallil I don't know if they still are together, but there was. London Calling!

Will Hunting

I think I will stop flagging my enemy, lol. Wasting my time, lol.

sarah

mom is such a stupid spelling

it should be mam

Khallil

It's actually 'mum'.

sarah

7:44 PM

@WillHunting who is your enemy?

@Khallil Where is the "u" in mother?

Will Hunting

@sarah I have a suggestion. You should change your username from sarah to Sarah.

@sarah I will email you later on.

Khallil

Where's the 'a' in mother, @sarah?

1 min ago, by sarah

it should be mam

sarah

@Khallil its in madam

Khallil

The last time I checked, madam and mother weren't the same thing, @sarah.

sarah

@Khallil you should always treat your mother like a madam

Khallil

7:46 PM

That doesn't change the fact not every madam is a mother, @sarah.

Madam

Madam, or madame /ˈmædəm/, is a polite form of address for women, often contracted to "ma'am". The abbreviation is "Mme" and the plural is mesdames (abbreviated Mmes). The term was borrowed from the French madame (French pronunciation: [maˈdam]), which means "my lady". == Use as a form of address == In speaking, Madam is used in direct address when the lady's name is not known; for example: May I help you, madam? In the United States and in English-speaking Canada, "ma'am" is usually used, except in regions such as New England where particular ties to England still exist. Even then, "madam" tends...

Alizter

@WillHunting I changed it. It was bugging me too :P

sarah

but every mother is a madam

mother + madam = mamam = mammary

-> mammal

Daniel Fischer

Hmm: Madam, a term for a woman who is engaged in the business of procuring (prostitution), usually the manager of a brothel