Mathematics - 2015-03-13 (page 5 of 5)

Owatch

22:10

Yes

Sorruy

teadawg1337

Sorry for what?

Owatch

$\sqrt(2)^5$

is $4\sqrt{2}$ like you said before

teadawg1337

Mhm

Owatch

I was cooking

AFK

I am back

ᴇʏᴇs

@Owatch What are you making

teadawg1337

22:11

wb :D

ᴇʏᴇs

@Owatch Is it French cuisine

Owatch

Hardly.

ᴇʏᴇs

Too bad

teadawg1337

Whatever it is, I want some. I'm starving

ᴇʏᴇs

@teadawg1337 I have macaroni and cheese

teadawg1337

22:13

Meh, not in a mac n' cheese mood today

ᴇʏᴇs

So you're not starving

teadawg1337

I'll just get a bowl of peanuts or something

@ᴇʏᴇs It's a little something called hyperbole...

ᴇʏᴇs

@teadawg1337 I know hyperbola

Owatch

$\sqrt{2+t^2}^5 - 8*\sqrt{2+t^2}^3 + \sqrt{2+t^2}+c$\

teadawg1337

What happened to the denominators, @Owatch?

Owatch

22:16

I did not include them.

teadawg1337

But what about 1/5 and 1/3

What happened to them?

Owatch

Isn't it 4/5 and 8/3?

teadawg1337

Yes, I was referring to the denominators themselves though

Owatch

Well, I though that since sqrt(2) was the denominator of sec in terms of x

I could remove from parentheses if I raised to power of 5

Or whatever power sec was raised to

teadawg1337

But there was nothing to cancel the 5 in the denominator

It should still be there, same with the 3 in the second term

Owatch

22:19

Oh right

I see why

Mistake using (wrong) piece of solution

I go back and fix

$\frac{(\sqrt{2+t^2})^5}{5} - \frac{4*(\sqrt{2+t^2})^3}{3} + 4*\sqrt{2+t^2} + c$

teadawg1337

There you go! I know you meant for that equals sign to be a minus sign

Owatch

Yes I spotted that, my bad.

teadawg1337

Although $\frac{8}{6}=\frac{4}{3}$

Alec Teal

$\udot$

Owatch

Okay, very nice.

teadawg1337

22:26

That's the correct answer, though it's not expanded

It's good enough, though

IMO

Owatch

If you want me to expand

you will have to kill me.

Moving on

teadawg1337

I don't want you to expand it

It's fine as is

Owatch

Good idea.

Back to other problem.

$\int{\frac{1}{t^2\sqrt{t^2-16}}} dt$

teadawg1337

This one's simpler than it looks. Set $t=4\sec(\theta)$

Owatch

I have

I will get differential from Mr.Wolf

Then plug in?

teadawg1337

22:29

?

Owatch

dt

Oh wait

teadawg1337

You can't differentiate $4\sec(\theta)$?

Owatch

I am thinking about something else

Yes

tanxsecx

teadawg1337

$4\tan(\theta)\sec(\theta)d\theta$

Owatch

Okay, I did not include 4, but know in my heart it was there

teadawg1337

22:31

That's not good enough in mathematics :P

Gotta include the 4

I guarantee you someone would count it wrong if you didn't include it

Owatch

Yea.

teadawg1337

Okay, so what does the denominator become?

Owatch

Working on it

$\frac{1}{16}\int \frac{1}{sec\theta} d\theta$

teadawg1337

\theta

That's correct

What's $\frac{1}{\sec(\theta)}$?

Owatch

$cos\theta$

teadawg1337

22:37

and what's $\int \cos(\theta)d\theta$?

Owatch

$sin\theta$

teadawg1337

no

That's the derivative of $\cos(\theta)$

There you go

Draw a triangle to put the equation in terms of $t$

Owatch

is sec reciprocal of cos?

teadawg1337

Yes

Owatch

Ah yes it is, I also looked at identities

Thanks

teadawg1337

22:41

$\sec(\theta):=\frac{1}{\cos(\theta)}$

Owatch

hmm.

Opposite side = $-\sqrt{15}$

from $\sqrt{1^2 - 4^2}$

teadawg1337

If $t=\sec(\theta)$, then $\theta=\arccos\left(\frac{1}{t}\right)$

What's $\sin\left(\arccos\left(\frac{1}{t}\right)\right)$?

Owatch

sec is reciprocal of cos. So adj/hyp = hyp/adj. Since $4sec\theta$ = t, then $sec\theta$ = t/4

teadawg1337

Oh, whoops

Owatch

I make mistake too, I write t as 1

On paper

teadawg1337

22:45

You're correct

I was wrong, that's a rare occasion

Mark it in the history books :P

Owatch

as usual

pfft

Ok, I fix my error too

teadawg1337

What's $\sin(\arccos(\frac{4}{t}))$

I did it again -_-

Owatch

$\frac{\sqrt{t^2-16}}{16t}+ c$

Is the answer

teadawg1337

Okay, so what's the answer?

To the integral

Owatch

I just edit above.

teadawg1337

22:48

What's it missing?

Owatch

The sea?

teadawg1337

The constant of integration

Not a large body of water, no

Owatch

I c.

teadawg1337

Any more integrals that you need to finish?

Owatch

Next four questions are Integration of rational functions by partial or something

But I won't do them today.

Tomorrow.

teadawg1337

22:50

Partial fraction decomposition?

Owatch

Sure.

Integration of polynomials?

teadawg1337

Integration of rational functions using partial fraction decomposition

Owatch

Yes.

That is what I shall do tomorrow.

I dislike them.

They are long problems.

teadawg1337

You seem to dislike everything in calculus

Calculus is the black sheep of topics in mathematics

Owatch

If I like something, I'll mention it

I liked doing problems where you take y' in a differentiation problem

Not sure what that was called.

teadawg1337

22:55

Differentiation?

ᴇʏᴇs

Hi @Mike

@Owatch Maybe implicit differentiation

Owatch

That's it.

infinitesimal

Did you take pre-calc?

Owatch

Keyword

@who?

infinitesimal

You

ᴇʏᴇs

22:56

@skullpatrol I didn't but I wish I did to build up my foundations more

Owatch

yes.

What was bad news for me was when I heard there was a Calculus 3

infinitesimal

:-) I see

Owatch

I did not know what came after 2, but I did not think it was 3.

teadawg1337

Oh, you ain't seen nothing yet.

Owatch

(IN TERMS OF CALCULUS)

teadawg1337

22:57

Just wait until you get to multivariable

Owatch

That looks bad on its own

ᴇʏᴇs

@Owatch Some schools have a calc 4

teadawg1337

Vector calculus is a pain, even for me (first time learning it, at least)

infinitesimal

and 5

Owatch

> I did not know what came after 2, but I did not think it was 3.
That looks so stupid.

Bib

22:58

Is a torsion-free group not necessarily abelian?

Owatch

@teadawg1337 Vector calculus?

Vector is dx/dy is it not?

ᴇʏᴇs

@teadawg1337 Do you know an easy multivariate/vector analysis book that covers tensors

teadawg1337

Noooooooo @Owatch

Flip to the last few chapters of Stewart Calc @Owatch

Owatch

A vector in high school physics was change in x, change in y related.

Let me look in book

teadawg1337

Last two chapters, actually.

Owatch

23:01

Infinite sequences and series?

Pi Day

HAPPY $\huge\pi$ DAY FOR THOSE WHO LIVE AT GTM+1!!!!

Owatch

Isn't it GMT?

ᴇʏᴇs

@PiDay How often do you change your username

teadawg1337

Huh, I guess it's not in the standard book. My mistake, it must be in just 7E: Early Transcendentals

Owatch

It is not

It's not in the index

user159870

23:02

HAPPY $\huge\pi$ DAY @PiDay

teadawg1337

There's still 6 hours left in the day where I am

Pi Day

@ᴇʏᴇs often

teadawg1337

@Owatch Hmmm... I know, look up Green's theorem on Google

Owatch

There is an integral with a circle in the middle

I do not know what that means

ᴇʏᴇs

@Owatch Probably an integral over a closed path

Owatch

23:06

Finding area of regions or something?

Pi Day

@Owatch le fail you're right q_q

teadawg1337

@Owatch Finding the area of a closed three-dimensional curve

ᴇʏᴇs

I wish the chat would not automatically load Wikipedia and take up half the page

Owatch

0_o

It looks 2 dimensional?

teadawg1337

It's beautiful, though..

Pi Day

23:07

@ᴇʏᴇs add something after the link

teadawg1337

That's just to help students understand the material better, I would assume

Owatch

Oh

I do not know if I will ever learn that.

teadawg1337

It was a bit challenging for me

Owatch

* I will never learn that

ᴇʏᴇs

en.wikipedia.org/wiki/Alexander_horned_sphere @PiDay

Owatch

23:09

I believe Calculus II or III is about as much as I will learn,

teadawg1337

Which is sad, because most people never need more than Calc I

Owatch

Why is it sad?

teadawg1337

The beauty in mathematics only shows when you get past vector calc

Owatch

I *not very good, even this is hard for me.

teadawg1337

Well, be glad I'm here to help you through the course :D

This chat is the next best thing besides asking your professor

Owatch

23:12

Professor doesn't speak English that well.

ᴇʏᴇs

Better than a professor in some cases

Owatch

Many people hate math.

In my college.

teadawg1337

@Owatch just sit back and relax today, and know that I'll be helping you work through partial fraction decomposition tomorrow

Many people hate math in general

Owatch

Maybe I get up early and try to solve it before you get up

-___-

teadawg1337

I get up every day at 6:00 AM (GMT-05:00)

Owatch

23:15

:<

Can you get up at 12:00 PM?

teadawg1337

No, I have a routine with my sleep. If I mess it up, I'll be groggy for a week

And spring break ends this weekend for me

Owatch

So does mine.

"break"

teadawg1337

What state do you live in? I know you said you're from France originally

Owatch

CT

teadawg1337

Connecticut? That's a bit north from here... I live in TN

Owatch

23:19

Yes that is far.

teadawg1337

We've both had a brutal winter, though

Owatch

Snow touches the road and everyone crashes down there.

teadawg1337

A bit of an overexaggeration there, but...

Hey, it's impossible not to slide around everywhere when there's an inch of ice and three inches of snow on top of said ice

Owatch

All NE tow companies move south for winter.

Because of the business.

jk

But I would if I were them.

teadawg1337

Just because the people living here aren't as used to winter weather as those who live in the northeast isn't enough to imply inferiority/superiority

Owatch

23:23

Inferior winter skills.

Well, it is amusing to see the chaos it causes.

And people who throw hot water on windscreens to melt ice?

teadawg1337

shrugs

Bib

Is it the case that every finitely generated nilpotent group has a finite index subgroup with infinite abelianization?

Owatch

You just need ploughs.

teadawg1337

@Owatch the cold was brutal on its own, though

Owatch

Without that roads are dangerous.

teadawg1337

23:24

Oh, we have snowplows down here, and salt

the last winter storm was difficult to prepare for, since it was raining for the entire day until it turned into winter precipitation

Any ice placed on the roads would've washed away with the rain

Owatch

I've done a good amount of sliding.

teadawg1337

Tennessee is really hilly, so it's great to go sledding and stuff during the winter

Owatch

I don't have sled.

But I did take walks a lot

I got stuck in a forest.

teadawg1337

D:

Owatch

I tried to take shortcut

teadawg1337

23:27

Did you get out?

Owatch

Yes. But it took me several hours

teadawg1337

At least you made it out, though

Owatch

I could see where I needed to go. But snow was waist deep and after an hour I was very tired.

I had my dog.

He was not helpful

teadawg1337

Well, at least you had some company

Owatch

Yes.

teadawg1337

23:30

Shouldn't you check on the dinner you're cooking soon?

Follow-up question, can I have some?

Owatch

Well it's done a while ago

It was finished when I came back

teadawg1337

Oh. What did you cook?

Owatch

Ham, and then some vegetable and chicken mix.

Not fancy

teadawg1337

Sounds good, though

Owatch

I guess. I'm going to take my break now

Go do other things.

Watch show maybe.

teadawg1337

23:32

Cya tomorrow, @Owatch!

Owatch

Bye

robjohn

2

Q: Real Analysis question about proving limits using boundedness and monotony

I am trying to get a hang of solving problems that ask to "prove the limit". One of the questions on our previous homework was: The solution starts with . How do we know that sn is bounded below and not above? I believe the next step is to plug in the formula for Sn+1 into Sn^2 - x >= 0 but ...

I started to answer, but then I fell asleep :-)

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$Mathematics$ Mathematics