@Socrates are you german?

@DHMO I thought that is clear by now. But why you ask?

(probably some cringy grammar)

that's an interesting use of "stand"

in german that doesn't even make sense, I think.

ah well

semi

you're probably right

$d(f)$ would make more sense

as you are taking the derivative of a function, or not?

ok im a bit confused why is e^(x/2) = 1/2*e^(x/2) i had always been told e^a was simply e^a so why isn't it simply e^(x/2) ?

@DanielFischer when is your book coming out? :-) (unless it already has .. )

chain rule

while defining boundedness for a subset $S$ of a topological vector space .. we require $S \subset \alpha U$ for all $\alpha \ge c > 0$ for 'every neighborhood' $U$ of $0$ .. is there an example of such a space where 'every neighborhood' is actually required (for example, if the space is normable .. only one nbd suffices)?

I have found the minimum of the function $g(x,y)=2x+y$ under the constraint $x\cdot y=18$. Is there a program where we can see graph of that?

So a computer is a universal machine that can do everything, combined with a screen that can do what the universal machine can't do

I mean, it's a universal Turing machine combined with a display monitor, and I'm pretty sure that the display monitor is magic.

@r9m so god can do anything, but human can do what god can't do(i.e. nothing).

where doing nothing is still a task. I mean how do you do nothing?

@MaryStar desmos.com/calculator/2bqg9spbhk

@LawrenceLelo How can we draw also the function $g$ ?

@MaryStar big hint: search plotter in google

otherwise, do it from scratch with the language of your choice

@Socrates So we cannot plot that function in desmos, can we?

It's possible. desmos.com/calculator/bulsuh5etz

@MaryStar 'beautiful free math' is their slogan. Draw whatever conclusions you like.

You can't directly plot multivariate functions. However,

someone has managed to figure out how to hack it into doing so.

Yea and you can't input anything involving infinity (which makes sense actually)

Slide around $a$, $b$, and $c$ in that (numbers 31, 32 and 33).

@LawrenceLelo You can still do integrals and derivatives, though

which are pretty close, since they involve limits.

Fun fact: Typing in $-\frac d{da}a!$ and then $a=0$ into Desmos will give you $\gamma$.

Ohh interesting

And $\frac d{dx}x!-\frac d{da}a!$ and $a=0$ will give you a smooth version of the Harmonic function $\sum_{n=1}^x\frac1n$.

hello! can some of you answer a very dumb and short question?

(The factorial function they use is related to the Gamma function.)

Could someone of you take a look at my question math.stackexchange.com/questions/2103721/… and tell what $\lambda$ is?

maybe it is defined somewhere in the script of your docent?

guys, really dumb and short: we know that if f'(x) > 0 and f''(x) != 0 x is an extremal value. Is this an equivalence or an implication? I would say it's the first but... is it?

The table below shows the probability distribution of the number of television is each house in a community

the question is asking the to find the probability that a house in the community will have at least 3 televison

@T_01 Consider $y=x^4$ at $x=0$.

Also, I hope you mean $f'(x)=0$ and not $f'(x)>0$.

(To activate LaTeX, use the link on the top right: tinyurl.com/cfqcvpc.)

But, in any case, for $x^4$, the first derivative is zero and the second derivative is zero.

So it's not an equivalence.

@AkivaWeinberger good work

for some reason I can't send the picture

so ill send the info

You can upload it to imgur and give us the link

ok

imgur.com/TG4C0vD

here

televisions 3 and 4 are X and Y

I tried finding like a pattern but I couldn't do that either for the probability

my guess is the numbers have to all add up to 1 and its less likely that people have 4 TVs than 3 so find two numbers that all the numbers add up to 1 then the smaller value goes to the 4 TVs

You can type http://i.imgur.com/TG4C0vD.jpg and it'll show the image

oh i didnt know that

Oh @WDUK but 3 and 4 are not known how would I equal them to one like .04

.04? what

I was going to say .04+.38+.27+x+y+.13=1

3 and 4both could be D

and then I don't know x and y so

add them all up it equals 1

so like guess and check from the given multiple choices?

look the table summaries 100% so find two numbers so all the numbers than add up to 1

so 3 and 4 must both be 0.09

@AkivaWeinberger yes, of course = 0... mh.. i see... im stupid

Oh @WDUK ok thanks

@T_01 No your not. It's often fairly hard to come up with counterexamples to reasonable-sounding conjectures in calculus.

A lot harder than showing that a certain function, that someone else gives to you, is a counterexample.

maybe, but this is not my real problem... i have another task to do, and im to stupid for that. if this would be an aquivalence the solution would be too ez, though

Ah. May I ask what that other task is?

(Though I should be studying for a test)

i start learning integration methods next week hope its not too difficult to learn

if you dont tell me the solution, i can ^^

@AkivaWeinberger can there be a counterexample that is harder to verify than to disprove it in the first place?

(numerical things aside)

how would I find 9/6=e^.065t

like I know it was ln something

@MATHASKER do you know about the natural logarithm?

base of 10?

hmm. wait, @Akiva im trying to fing out how to use latex here xD

'natural' logarithm

no

@Socrates Does the counterexample to the conjecture that an irrational number to an irrational power count?:

@MATHASKER then search natural logarithm of $e^x$ in google

Where we know that either $\sqrt2^{\sqrt2}$ or $(\sqrt2^{\sqrt2})^{\sqrt2}$ works, but it's hard to verify which @Socrates

ok i have it ^^ so i try to write it down now

@AkivaWeinberger this one semi gave me, as I recall. And I don't understand the problem by now^^ (to judge which is it)

test.. $D-3$

oh working :D

@AkivaWeinberger is it already solved which one is it? just asking ;)

(please dont say which)

Yes.

... $D \psubset\ R$

@T_01 Test: $\displaystyle\sum_{n=1}^\infty\frac1{n^2}\in\pi^2\Bbb Q$

how do i write psubset?

its working now, but is this "real" latex?

@T_01 For subsets use \subset $\subset$, \subseteq $\subseteq$, or \subsetneq $\subsetneq$

isn't $(a^b)^b=a^{(b^2)}$?

mh... ok

@Socrates Yeah.

The question is, is $\sqrt2^{\sqrt2}$ rational. @Socrates

is there a list for the latex commands for this chat?

do we know, that only one of those is rational?

Professor Google

yes, but there i found \psubset for example and this isnt working :D i search another one....

mathjax is not latex

it just happens to be that mathjax is very compatible

oh k

Anna and Zach each have 600 to invest. Anna's investments earn a rate of 10.5% and Zach's investments earn a rate of 6.5%. Approximately, how much more money will Anna have than Zach when Zach's investments are worth 900?

@Socrates Certainly only one of them is an irrational raised to an irrational equal to a rational.

for this I tried to first find time for Zach

using the Pe^rt

But i think thats wrong, how would I go on to solve this

And it is known that $\sqrt2^{\sqrt2}$ is, in fact, irrational. It's a hard theorem (that I haven't tried learning).

well, $\sqrt{2}^2=2$, so we know the exponent of $(\sqrt2^{\sqrt2})^{\sqrt2}$

and then its simply 2

So $(\sqrt2^{\sqrt2})^{\sqrt2}$ is rational (it's equal to $2$), and is an irrational raised to an irrational.

But we need the hard theorem for that.

is the stuff in the bracket confirmed to be irrational?

Yes

(I mean, I haven't tried learning the proof.)

more reading hehe

how is the conjecture called?

@T_01 Close the dollar signs. For $\Bbb R$, use either \Bbb R or \mathbb R.

to include text in the $ signs, take \text{your text}

sigh

And for $\to$ use \to (or \rightarrow, but \to is better)

$\rightarrow\Rightarrow$ test

For \sin(x), use \sin(x). Compare: \sin x is $\sin x$; sin x is $sin x$.

can some one explain that second part of d/dx

why isn't it just x^2

haven't i already done the first function yet this book is doing it again =/

i had 3cos^2(x^2) *2x

The derivative of $(\text{stuff})^3$ is $3(\text{stuff})^2\,\cdot\,\frac d{dx}\text{stuff}$.

@WDUK I think it should came after cos

(You have LaTeX on, right?)

Here, $\text{stuff}=\cos(x^2)$.

yeh its on

but isnt x^2 stuff aswell ?

cos(stuff)

so i have 3 chains here not 2?

Yeah, but it's inside the cosine so you need to deal with that, too.

ah okay

Yeah, it's going to end up being 3 chains

jeese this is tricky stuff

because the $\frac{\rm d}{{\rm d}x}\cos(x^2)$ needs the chain rule itself.

Think of it this way. How would you calculate $\cos^3(x^2)$? "I'd take $x$, and first square it, then cosine it, and then cube it."

$x\mapsto x^2\mapsto\cos(x^2)\mapsto\cos^3(x^2)$

So first we do the derivative of the cubing, then times the derivative of the cosine, then times the derivative of the squaring:

$$\left(3\cos^2(x^2)\right)\cdot\left(-\sin(x^2)\right)\cdot\left(2x\vphantom{^2‌​}\right)$$

ok so -6x * cos^2(x^2) * sin(x^2) is what i get

That's what I get, too

okay going to practice some more ^_^ thanks for the help

Having used Lagrange multipliers to find that the function has a extremum. To check if this is maximum do we use the second derivative test?

hey guys can any one help me with this problem

Anna and Zach each have 600 to invest. Anna's investments earn a rate of 10.5% and Zach's investments earn a rate of 6.5%. Approximately, how much more money will Anna have than Zach when Zach's investments are worth 900?

I tried to find the time first by using zach

and the pe^rt formula

But I think thats wrong

There is a limit what a human can parse per time. So when one says humand judgement will always be superior to an algorithm processed by a machine, one implicitly says that a machine can't parse more per time than a human. Because if it could, there are certainly cases where the judgement of a machine is superior.

We have better built-in heuristics.

Wait, no

Our heuristics are horrible. That's why logical fallacies exist

(and there are so many of them!)

otherwise, maybe my premise is false

maybe humans can parse close to infinity informations per time

and we didn't discovered ways to do it

(infinity is excluded, because well, brains are finite)

maybe let's start at: can a finite set of particles contain infinite information.

We're not doing Gaussian elimination to make judgements

or anything like that.

@AkivaWeinberger we could exclude numerical things. and focus on logic.

but even then, logic seems an area where machines are superior

except... fuzzy logic

I dunno. I feel like we need a concrete case before philosophizing.

mmh

Computers are built on logic. (Though I think Stephen Wolfram says it's not necessary.)

I think creating a concrete case is maybe harder

no, a finite set of particles cannot contain infinite information.

@T_01 prove it

and therefore... welcome back skysoldier, you got really just muted for the "f" word for 30 minutes -.-

@T_01 lol, didn't recognize skysoldier^^

prove? define information first

mhh -.-

instant ban

@T_01 touchè

touche?

soo... @AkivaWeinberger ... back to the task... xD

defining information is hard

you cannot ask an question without definig things used in there :) so ez it is

Write information in ASCII. Put it after a decimal point, to get a number between 0 and 1 corresponding to the information.

Place a ball exactly that number of meters away from this wall.

@T_01 I will follow this.

Or, exactly that proportion between these two points.