Hello. Do you think it's okay to add hand drawn pictures to my question? Nothing nsfw, just examples of graphs. They're too simple for me to wanna go explore drawing software just because of this, but I don't want to hurt anyone's feelings either... drawing stuff by hand left and right you know

petya: i personally don't see anything wrong with it. people are more likely to care about how the image is being used than where the image comes from (i.e. hand drawn or with software). it is very helpful if the image is not absolutely necessary for stating the problem (i.e., the image may assist in understanding the problem, but you wouldn't necessarily need to interpret it to understand what is being asked).

if you absolutely need the picture to understand the problem, there are accessibility concerns you might expect some people to complain about (e.g. visually impaired users, or users on certain devices, may be unable to get the problem at all, which is not ideal). putting accessibility aside, it is also often just very difficult for people to interpret images or give useful feedback on them without a lot of back-and-forth, which can affect whether anybody bothers to respond

i have a problem with it.

especially the sfw part.

jk ofc. hand drawn is perfectly fine and has more character.

haha

@leslietownes By any chance can you help me with my question?

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However on the phone (not desktop mode) when you delete a message, the text is the same color as the text of a normal message

On desktop mode / PC the first message should be light grey

@BinkyMcSquigglebottom do you want to blind us? :(

$$\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi, \pi, \rho, \sigma, \tau, \upsilon, \phi, \chi, \psi, \omega, \Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Upsilon, \Phi, \Psi, \Omega, \pm, \times, \div, \neq, \leq, \geq, \approx, \equiv, \sqrt{x}, \frac{a}{b}, \int_{a}^{b}, \sum_{i=1}^{n}, \prod_{j=1}^{m}, \lim_{x \to a}, \sin(x), \cos(x)$$

🤡

(⁠╯⁠°⁠□⁠°⁠）⁠╯⁠︵⁠ ⁠┻⁠━⁠┻

$ \Huge 🤡$

$\Huge \text{ Hi Sine of the Time}$

@BinkyMcSquigglebottom try ctrl w to enlarge the text

Ok let me see

@SineoftheTime $\tiny 🤡$

my tab closed

🤔

However the 🤡 I sent were ironic, I hope you understood :-)

Hello everyone, I have encountered a problem. When I study the function $f(x) = e^{\sqrt{\left|\frac{x-2}{x+2}\right|}}$, both my professor and I get $\lim_{x \to -2^{+}} f'(x) = - \infty$, $\lim_{x \to 2^{-}} f'(x) = - \infty$ and the function is monotone decreasing in the interval $]- 2, 2[$.

The problem is that if I calculate the second derivative, it is greater than $0$ in the interval $]- 2, 2[$, so the function is convex in that interval (I plotted the function on Geogebra, Mathematica and they confirm this). But my professor says that if $f$ were convex in $]- 2, 2[$, then $f''(x) > 0 \forall x \in ]- 2, 2[$, i.e. $f'(x)$ is increasing in $]- 2, 2[$, and this is absurd because $\lim_{x \to 2^{-}} f'(x) = - \infty$. What is the truth?

is $f''(x)>0$ for all $x\in ]-2,2[$ ?

@SineoftheTime Yes, but the derivative is too long to compute, so my professor searched an alternative method...

the function is not convex in $]-2,2[$

@SineoftheTime How not? Try plotting it in Mathematica or Geogebra...

@Bml not sure how you are getting that f''(x) is positive in (-2,2)

even desmos shows that it turns negative at around x=1.414 (presumably x=sqrt2)

@Bml I did and it's not convex near $x=2$

@SineoftheTime Could you put the graph here and show me where it is not convex between -2 and 2? It may be that I got confused....

@Bml desmos.com/calculator/inzwukyrjj

You know that if you enter f(x)=... into desmos you can then just graph f'(x) and f''(x) ? @Bml

@BinkyMcSquigglebottom how do you do it? By putting $\frac d{dx}$ or there's a different syntax?

@SineoftheTime It is both convex and concave...

literally just type f'(x) and f''(x) in @SineoftheTime

@BinkyMcSquigglebottom thanks, I should learn how to use desmos properly

@Bml $f''(x)$ is not always bigger than $0$ in the interval

@SineoftheTime OK, how to figure out in which intervals it is concave and in which intervals it is convex? It seems to me that between $-2$ and $0$ it is convex...

near $x=2$ is not convex

@SineoftheTime Is that the only neighbourhood where it is not convex?

you should study $f''$, but why is it relevant?

well for x>sqrt2 its not convex

your mistake was thinking $f''>0$ in the interval, so there's no contradiction

@BinkyMcSquigglebottom Yes yes, I made a mistake in the calculation :-)

I am starting my semester no 5, and I'll send in the course catalogue:

is this feasable? as in, it took me 2.5 months of my summer holidays to finish 2 chapters of Rudin and 3 of Hoffman. So i am not sure how one can complete this many courses in such a short span

Sem 7 and 8 will be a bit hard

@nickbros123 Where? In the US, I would generally advise students to avoid taking more than 18 credit hours in a semester (and generally advise that they stick to around 15 most semesters).

Most bachelors degrees in the US are around 120 credit hours, so 15 per semester gets you out the door in 4 years. It looks like you are in a combined BS/MS program, which I would generally expect to take around 6 years. I would generally advise a student to take only 9 graduate (i.e. masters/phd level) credit hours in a semester, with an absolute cap of 12. So semester 9 looks like a challenge.

And semester 8 looks insane.

lol

But this is advice for US students at a typical US college or university. I have no idea of the structure of your institution.

180 credits in three years in Italy :(

@SineoftheTime I can't imagine that being at all feasible, unless credits are counted differently.

1 credit is usually 8-10 hours of lessons

@SineoftheTime As in, 1 credit is 8 hours of lecture?

In the US, one credit hour roughly corresponds to 1 Carnegie hour of lecture per week, for 16 weeks. So 1 credit hour is 16 hours of lecture.

I've seen the estimate 1 credit = 25 hours of work (including both lectures and studying at home) used both in Italy and Germany

I've also heard the estimate 1 credit=25 h

@AlessandroCodenotti In the US, I generally tell students that 1 credit hour should correspond to around 3 hours per week of work (including lecture, homework time, etc) for a semester, or around 48 hours total.

the bachelor is 180 credits and the master 120 credits

So it sounds like 1 US credit is about the equivalent of 2 Italian credits. So 180 Italian credits in three years is the equivalent of 90 US credits in 6 semesters, or around 15 US credits per semester. So it comes out about the same.

@SineoftheTime Given that most European institutions tend to omit general education / the liberal arts, this sounds about right.

You're supposed to do 30 credits per semester/60 credits per year but of course it's common for students to take a bit longer

expecially math, physics and engeneer degrees

@nickbros123 Still curious to know what institution this is from / where in the world you are.

India?

@XanderHenderson india, an IISER

@nickbros123 Oh, I have no clue how the Indian system does anything.

I don't know what an "IISER" is, for example.

if anyones interested, check page 164 and above for further details iisertvm.ac.in/files/read/course-catalogue-22-23

these 3 credit courses correspond to 40 hr semesters

of lectures

@SineoftheTime Is it not advisable or necessary to study the second derivative? It's very long to compute...

Do you have to study the function?

@SineoftheTime Yes, but it was not in the requirements of the exercise to calculate the second derivative. However, it was required to plot the qualitative graph, and without the second derivative, how is that possible? It doesn't seem possible to get $\sqrt 2$ without studying the second derivative...

I have a basic question. Can a power series be defined at the edge of the radius of convergence, i.e. at $x=c\pm R$, but the derivative of the power series may not be defined there?

@psie consider the series \sum_n x^n / n^2 , this is gonna be defined on the boundary of its convergence radius, but the seriers of the derivative will diverge at x=1

ok, scary. Seems like anything can happen on the edge.

Anything can happen when you're on the edge. How power series teach us about life

boundaries are where the fun is... unless you are in the interior of a jungle

Holy sh*t.

Trump got shot.

that's sad

you never know, it could be a stage show.

Oh, now Elon is endorsing Trump. :eyeroll: