OK, going shopping ... Bubye for now.

later

I'll give it a shot, @Ted! Have fun shopping. ^_^

@Khallil Can you help to understand how can I compute $lim_{x\rightarrow 0^+} (x+2)\exp(1/x)$? Intuitively I would say is $\infty$ but how can I prove this ?

First see if you can simplify out the x+2 factor @Yasser

I was just going to recommend that!

I guess "simplify" is not the right word, but find a way to get rid of it

Expand?

No, not what I have in mind

@KarlKronenfeld Ah you mean that $(x+2)\exp(1/x)\sim \exp(1/x)$ ?

right

@KarlKronenfeld Thanks.

The problem now lies with $e^{\frac{1}{x}}$.

using the definition of what is $lim_{x\rightarrow 0^+}$ or $lim_{x\rightarrow 0^-}$ I think I can conclude that is $+\infty$ and $0$.

Oh!

for $lim_{x\rightarrow 0^-}$ @Khallil

I didn't the see the negative superscript!

lol , no problem :)

I need a lot more practice.

Have you got any more limit questions, @Yasser?

As me..

I think I solved all my problem for today @Khallil, thank you for your time.

Don't worry about the question, @Yasser. It was more of a philosophical question, so I edited it and will post it in the philosophy chat.

Have you got any others ... for me, @Yasser? =P

I need the practice too!

haha! I am tired, I am apart from any linguistic subtlety now ;P

Have you an idea please: math.stackexchange.com/questions/914239/direct-sum-on-homology]

@Khallil Are you from maroco ?

please don't downvote juste give me idea please

I am indeed, @Yasser. Where are you from?

@Vrouvrou It's beyond my reach..

Mine too, @Vrouvrou.

@Khallil France but I am of Palestinian origin.

I have many Moroccan friends :)

That's a pretty cool mix, @Yasser. By 'from', I assumed you were referring to my origin. I live in the UK but I'm of Moroccan origin.

I like France.

Are you reading a certain text on limits, or are you just plucking random questions off the internet, @Yasser?

@Khallil Yes that's what I mean. Oh I am playing football manager and I took Newcastle , this is off topic, I know lol. No, I have an exam on monday @Khallil. I am trying to solve some annals.

perhapes @robjohn can help me ?

And sorry for my English @Khallil , I try to improve myself.

Annals, @Yasser?

old exams ?

No prob! I'd be even more sorry for my French!

Oh, I see.

So I'm pretty stressed out, I hope I will succeed to integrate(?)

Integrate? Is this exam going to help you get into a school?

Or are you going to integrate as in $\displaystyle\int$?

Lol, yes this exam is going to help me to get into a school.

Ah. All the best of luck! I believe in you! ^_^

Tank you very much!

I am going to sleep, Good night @Khallil.

Good night, @Yasser!

see ya later :-)

@r9m I'm sure there is, I will try to work on this later today.

@Vrouvrou we are going out to lunch now. Perhaps later.

@robjohn :D okay !! :D

enjoy your lunch

hello, @Karl, though you seem to be gone now

I got it after successive (easy) uses of L'Hôp, @Ted. $$\lim_{x \to 0} \ \dfrac{1}{\sin^2 x} - \dfrac{1}{x^2} = \lim_{x \to 0} \ \dfrac{x^2 - x^2 + \frac{x^4}{3} + \dots}{x^4 - \frac{x^6}{3} + \dots} = \dfrac{1}{3} $$

hi @MikeMiller

@MikeMiller: Great app.

@Khallil: no need for L'Hôpital. Use basic algebra and the first week of calculus.

Let $x_n $be a real number sequence. We can create a sequence based on x_n of the supremums and infimums of x_n starting at gradually increasing indexes. So, lets do it.$A_k = sup{x_1, x_2, x_3, ...}, sup{x_2,x_3,...}, ... $ and $ B_k= inf{x_1, x_2, x_3, ...}, inf{x_2,x_3,...}, .$.. . Now, inf { $A_k$ } is what we call limit superior of $x_n$ and sup { $B_k$} is what we call limit inferior of x_n. Does anyone know one a property that our sequences $A_k , B_k $hold that uniquely defines them ?

Oh yea. Just multiply through by $\frac{\frac{1}{x^4}}{\frac{1}{x^4}}$

Heyo @Ted.

Dunno if you saw, but I think I got your hint from yesterday: consider the upper or lower triangular matrices.

I'm sure there are plenty of other examples

Yes, @Andrew, that's ok ... Or the subgroup of diagonal matrices ?

well, isn't that just the center?

oh, nevermind. yes.

No, the center is all scalar multiples of the identity.

Right

@nerdy: What you've typed is ununderstandable.

hello

Heya @Mike

Sorry, i can't manage to write A_k = sup{x_1,x_2,x_3,...} , sup{x_2,x_3,...}, ...

in Latex

@TedShifrin I'm sick of studying for quals. Only another 3-4 weeks of this...

I still don't understand.

What are quals, @Mike?

Hang in there, @Mike, once it's done you'll never have to go through it again.

I spent my whole first year doing it, @Mike, and our grad students often spend 2+ years, so stop your bitchin'.

@TedShifrin I've been doing it for at least six months, but good point, I'll only whine out of your earshot. :P

If you don't pass them all, you'll keep whining .. But louder :D

No matter how far I go, you'll still be within earshot of whining that loud @Ted

^ Quals.

What do you have to do for quals?

take a test

pass it