Let [math]f(x) = (x if x < 0) & (x + 1 if x \geq 0)[/math].
The function is not continuous (because in [math]x = 0[/math] we have a jump discontinuity), but is the function still differentiable?
For [math]x <0 [/math] we have [math]f'(x) = 1[/math] and for [math]x > 0[/math] we also have [math]f'(x) = 1[/math].
Furthermore we have [math]\lim_{h\to 0^-} frac{f(0 + h) - f(0)}{h} = \lim_{h\to 0^-} frac{h}{h} = 1[/math] and [math]\lim_{h\to 0^+} frac{f(0 + h) - f(0)}{h} = \lim_{h\to 0^+} frac{h + 1 - 1}{h} = 1[/math], so we have [math]f_{-}^{'} (0) = f_{+}^{'} (0) = 1[/math], so isn't it differentiable [math]\forall x \in \R[/math]?
But every function that is differentiable is also continuous, isn't it? Where did I do wrong?
Thanks
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Let [math]f(x) = x if x < 0[/math] and [math]x + 1 if x \geq 0[/math].
The function is not continuous (because in [math]x = 0[/math] we have a jump discontinuity), but is the function still differentiable?
For [math]x <0 [/math] we have [math]f'(x) = 1[/math] and for [math]x > 0[/math] we also have [math]f'(x) = 1[/math].
Furthermore we have [math]\lim_{h\to 0^-} \frac{f(0 + h) - f(0)}{h} = \lim_{h\to 0^-} \frac{h}{h} = 1[/math] and [math]\lim_{h\to 0^+} \frac{f(0 + h) - f(0)}{h} = \lim_{h\to 0^+} \frac{h + 1 - 1}{h} = 1[/math], so we have [math]f_{-}^{'} (0) = f_{+}^{'} (0) = 1[/math], so isn't it differentiable [math]\forall x \in \R[/math]?
But every function that is differentiable is also continuous, isn't it? Where did I do wrong?
Thanks
>>
[math] \begin{cases}
x & x < 0 \\
x + 1 & x\geq 0
\end{cases}
[\math]
Fuck latex man
>>
I'll write it plaintext:
f(x) = x if x < 0
x + 1 if x >= 0
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infotread?
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Anonymous
Understanding Exponential Functions 2016-11-22 17:16:09 Post No.8490158
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Understanding Exponential Functions 2016-11-22 17:16:09 Post No.8490158
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Understanding Exponential Functions
Anonymous
2016-11-22 17:16:09
Post No. 8490158
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Okay I've been working on this for some times now, and I simply can't figure out if my assumption is correct or not, pic related.
Let's say I want to find f1(x) where x=-1.
Do I simply use this calculation
a=ˣ2-ˣ1√⎺y2/y1
y2 or y1
b=————
aˣ
and use the point on the chart as (x1, y1) = (2, 0) and (x2, y2) = (1, 6), then use the f(x)=b∙aˣ calculation where x=-1?
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>>8490158
No-one can help you unless you provide enough information to explain wtf you're talking about.
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>>8490176
I'm making an assumption that the exponential function can be found using the presented calculation and wanted confirmation on whether or not I'm doing it correctly.
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>>8490201
Never mind figured it out.
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If there is a known cancer, would the resulting higher Igf-1 levels from exercise be worth the activity knowing that Igf-1 encourages cancer growth?
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>tfw no lgf
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>>8490146
There's a compromise. Same goes with calories. Nobody really knows, and you should be able to just kill the cancer instead of doing stupid balancing acts to stay alive a month or two longer.
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>>8490162
but is it true that with a lower igf-1 level, the cancer will grow at a slower pace thus more of a chance that the immune system can kill the cancer cells at a faster rate than the cancer cells can multiply?
Does melted water have health benefits? My local bookstore contain only two books by ignoramus about this question therefore I full of questions.
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>>8490016
What? That is a tautology, because water is the liquid phase transition of H2O.
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>>8490016
It staves off dehydration.
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Water can only get so hot before it becomes steam, it won't melt
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Give me ONE good reason to use RPN
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It eliminates the need for parentheses
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Dunno, I never used anything else.
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It will make your friends think that you are more inteligent than you actually are
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>tfw took a functional programming course this semester
>have to sit with CS spergs
>more than half the class failed the midterm
>they're still here
>mfw
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>>8489167
>>8489091
>>8485489
The butthurt is real
>>
Why would they leave?
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>>8489232
functional programming isn't even that useful
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Why the fuck would anyone major in computer """science"""?
Why would you want to work as a code monkey with pajeets your whole life?
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>>8489167
Because, you might decide to double major and desire a job with $200,000 starting as a data scientist.
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>>8489167
>Why would you want to work as a code monkey with pajeets your whole life?
Yeah, beats being an unemployed math/physics major.
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>>8489184
as if knowledge isnt the most important thing
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What do you guys think of American inventor of electricity, Nathaniel Tesler?
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>>8489101
Not even wheel got ever invented in murrica.
Since, like, first ape fell down in africa, it was a dumping ground for cowards that were hunted through asia and got lucky when bering strait could still be passed.
It got even worse some five hundred years ago when old continent started deporting criminals, whores and wackos.
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That's Hassan Kamel Al Sabbah, a famous Lebanese electrical engineer. He invented the television.
Nice multi-board shitposting OP
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>>8489101
Royally cheated and wronged by edison more ways than you could count.
Decent engineer.
AC is kind of useless now and we'd be better off if we had a DC infrastructure.
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The days of learning German for a couple of hours every day for a year are finally coming to an end. I'm moving to Austria in about few months to start university for the first time. I will study mechanical engineering there. I'm originally from Croatia.
I developed a late interest in physics and since I was a shitty student and never studied math properly, I decided to spend a gap year studying high school math from the start all the way up to calc, in order to be able to begin understanding physics once I start learning it in the university. (didn't study at all during high school, so that includes physics, even though I had a huge interest in it)
My initial plan was to study physics, but the crappy job prospects stopped me from pursuing physics, and instead I opted for engineering, thinking I'll have a job AND be able to attain physics knowledge. Now here is my current plan: move to Austria, find a dormitory, find a job to support myself and also have some money sent from the parents to help out, and get raped by lectures in German since I'm not fully proficient.
My heart lies with physics, I want to learn it all, but I'm afraid I fucked up big time. I'm afraid I'll never learn it completely since I'm going for engineering. The biggest joke is that I decided to merge two areas of passion, physics and languages, and I thought, why should I solely focus on languages throughout my life and become some translator, why not a physics/engineer and make languages a hobby?
Tell me how fucking stupid I am. Can I learn all physics during my studies? I also want to read Feynman's lectures, but my math ability in certain areas is still dodgy.
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>>8487473
Go with mechanical engineering, physics became a glorified math monkey field with idiotic theories that exist only to support one another, it is like architecture to civil engineering. You'll do better in mechanical engineering and once you settle financially you can always pursue physics in the later age.
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>>8487473
I give 0 fucks about this
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>crappy job prospects
>with fucking physics
Jesus, anon, just go for physics, you will get a good job with it and if it really interests you, fucking go for it.
I study physics myself at the TU Wien, if you decide to study physics, you will get a whole load of math in the first 2 semesters, it will be too hard for you at first if you aren't a mathematical genius. Don't let these courses overwhelm you, most people take the exams for Analysis 1&2 in the 6th semester
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How do I get an A in O-chem?
I did well in gen-chem, got As both semesters, but now I'm taking Organic Chemistry I and it's kicking my ass. I usually studied out of the book and grinded homework problems and just reviewed for 2-3 days before tests and did well, but now that strategy doesn't seem to work.
The tests are WAY more complex than the homework. While a homework question might ask for the major product of just 1-2 reagents + a solvent, the exams will ask for the major product after 5-7 reagents. Or we'll get stuff I have simply never seen before and I'll have no idea how to do it.
I don't *think* I'm a brainlet, but our class averages are around 30-40% and I'm BARELY getting higher than that, in the B range mostly when you include standard deviation.
I do like this class, at least. It's the most interesting class I have. But, goddamn, it's hard. How do I do well? The final is in 3 weeks.
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Try to see the overarching mechanistic patterns reactions have in common instead of trying to memorize each individual reaction.
t. orgo tutor
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>>8487182
Also yes ochem tends to require more effort than the first year courses. Studying more than 2-3 days in advance helps tremendously.
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>>8487182
Also, try to understand the underlying forces or hindrances, such as electronegativity and steric effects. Understanding why a certain mechanism goes a certain way makes them easier to undertand
t. been there done that
This is Barron Trump's age and height (unconfirmed - closest estimate) plotted on a growth chart.
How is this even possible.
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HGH
Hes rich
His parents are tall
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>>8489473
1 in 26,651,649 10 year olds are taller.
ie. almost none.
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>>8489482
Doesn't rule out HGH
Although this is anecdotal, my rich friend in high school was around 5'9" at 16 when his parents put him on HGH. Now he's 6'4" at 20. Regulated shit works wonders, god damned kikes
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Has anybody ever gotten a PhD in Math and a PhD in Physics? I remember reading about some Euro on here someone posted about and I think he had done so - and even had more PhDs
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>>8487347
Those kind of people are too smart for this board, literally.
Or they end up living for education, they never stop learning and there's a chance they will never have kids or getting married
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>>8487355
>they never stop learning and there's a chance they will never have kids or getting married
That alone is a proof that they're smart.
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>>8487364
I know right
Even Paul Erdos never got married and had kids, he called anyone that was married "a slave" and when someone is divorced he is a "free man"
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Friendly reminder that the NASA team behind testing the EM drive just postulated it had to do with PILOT WAVE THEORY and physics is about to be finally blown wide open and built from the ground up again as it should have been long ago.
Glorious pliot-wave masterrace coming through
>Anon, don't waste your career studying a fringe hypothesis like pilot-wave you are very bright and can really make something out of yourself
Hahahaha look who got the last laugh now?? Shut the fuck up and don't tell me what to do bitch
>The particle must simultaneously travel through both slits and bounce off itself
Holy shit how can your model be so retarded and obviously wrong? Einstein knew that shit was wrong.
Pilot wave theory was so obviously perfectly elegantly the correct answer this whole time and those that defended the Copenhagen model should be extremely embarrassed.
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>>8484346
The NASA team basically admitted they have no idea what they're talking about. They published in a journal that does not have relevant expertise. If this is your evidence for pilot wave then it only proves how weak it is.
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>>8484346
Pilot Wave a shit
>>
>believing in the ramblings of French madman
Anonymous
/sci/ would you say intellectuals are detached from science? 2016-11-22 14:43:13 Post No.8489990
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/sci/ would you say intellectuals are detached from science? 2016-11-22 14:43:13 Post No.8489990
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/sci/ would you say intellectuals are detached from science?
Anonymous
2016-11-22 14:43:13
Post No. 8489990
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The title is suggestive, didn't know how to put it differently. We are talking of course about intellectuals in general.
From experience with /lit/, the media and political boards on the internet is that - in general - they are immersed in their own world and own theories. Which is fine, but I find it a problem when those ideas and theories do not fit what I read about science. Especially when these ideas and theories are practised.
Of course the opposite may happen as well, that science is misused instead or distorted. Not all science is settled either so using unsettled science as a foundation for discourse might be a problem too.
What does /sci/ think? I think there should at least be some scientific foundation behind ideas, and more important no conflicts between ideas and what science shows.
I am not in favour of scientism. Values and meaning lie beyond the scope of science, though I do think some scientific foundation behind such things wouldn't hurt. I would like to mention as well there is also a limit to what we can know.
How does /sci/ look at this? Or are you fine with the current situation? Do you think that the misuse or distortion of science is too great and thus it is better if 'intellectuals' are stuck within their own world? Do you agree they are stuck in their own world?
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>>8489990
>Do you think that the misuse or distortion of science is too great
This should be:
>Do you think the potential for misuse or distortion