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/sci/ - Science & Math

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1595569 No.1595569[DELETED]  [Reply] [Original]

Could somebody please tell me if this is convergent or divergent and if convergent what is its value? Not a homework thread; school's finished, bro.

<span class="math">\int_{0}^{1}e^x/(e^x-1)[/spoiler]

Thanks.

>> No.1595578
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1595578

>> No.1595586

It's not convergent.

>> No.1595587

>>1595569
just use mathematica

>> No.1595588

Divergent

>> No.1595593

>>1595588
>>1595586

If it is I am verrrry happpppy. My final was yesterday. I did all the work, got messy then just wrote DIVERGENT in big letters. You guys sure??

>> No.1595597

>>1595593
100%

>> No.1595599

This is a definite integral. Convergence is not the word you are looking for.

There is an underlying question of <span class="math">\lim\limits_{x\to \0^+}e^x/(e^x-1)=\infty[/spoiler]. I assume that's what you mean by asking about the convergence.

>> No.1595600

>>1595593
I was lazy and used Mathematica, it said it didn't converge with those bounds.

>> No.1595610

>>1595569

\int_{0}^{1}{e^x\over e^x-1}

Fix'd (I hope)

>> No.1595612

>>1595610
Ah goddamnit

<span class="math">\int_{0}^{1}{e^x\over e^x-1}[/spoiler]

>> No.1595613

wolfram alpha?

>> No.1595618

>>1595599

Actually it is improper, not definite because of the asymptotic behaviour about the y-axis. Can't divide by zero.

It's called a Type II improper integral.

>> No.1595621
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1595621

There you go

>> No.1595631

>>1595621

Thank you woop woop ok. Not bad.

I know I fucked up the first, supposed to be easiest question ROYALY.

Domain of y=arcsin+lnx

I am fucking stupid. Fuck.

Forgot to look over that stuff. WHATEVS.

The rest went ok. As if you guys care. :)

>> No.1595634

>>1595618
Improper integrals are limits of definite integrals.

>> No.1595640

>>1595631
Did you get (0,1]?

>> No.1595642

>>1595634

Well yeah I know. But that guy man, he just got to me...

>> No.1595648

>>1595642
I don't blame you. The way I stated that was pretty stupid.

>> No.1595649

>>1595640

No and I know that's the answer and I know why and it's obvious, it's the only reasonable possible answer but I AM FUCKING STOOOOOPID AND I WROTE SOMETHING COMPLETELY DIFFERENT HE'S PROBABLY GONNA MARK THE FIRST QUESTION WRONG AND THEN TEAR UP THE TEST BECAUSE I AM A USELESS SCUMBAG RETARD

>> No.1595652

>>1595648

What I said to myself. i wrote arcsin's domain right, and lnx domains right. Then thought for some reason it would be the sum of their domains (fucking stupid idiot i am).

Then my prof notices and warns me that i'm wrong (nice guy which is why i feel so fucking stupid)

But I thought he pointed at my lnx domain SO I CHANGED IT TO (-inf, 0)U(0, inf)

AND WRITE IT'S DEFINED EVERYWHERE

why did I fuck that one up so bad? whyyyyyyyyy?

>> No.1595668

>>1595652
Everywhere but 0. At the very least, the single point at which you said it wasn't defined, it isn't defined. If he's nice enough to give hints, he might be nice enough to give a pity point or two. Did you leave the part where you gave the domains of each? That should get you some credit too.

And look at it this way: you won't fuck this up again.

>> No.1595701

>>1595668

Yeah, it was out of five so I will get a point for arcsin's domain. I would have gotten a point for lnx's domain but I erased it. Maaaaaaaaaybe he'll give me 2/5 because I wrote the definition of lnx in integral form. (it looks like it should be defined everywhere but zero when looking at the integral)

But yeah man. I said that exact thing to myself as soon as the exam was over and i looked up the definition. Never again will I hesitate in a similar question.