stupid questions that don't deserve their own threads -/qtddtot/-

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>>8442914
How do I solve for currents here? All resistors with the exception of the middle one are 2 ohm.
The center and right voltage source are 6 V while the left one is 3 V. I tried using Kirchhoff but to no avail, my system had multiple solutions. I probably screwed something up.

>>8442923
Use superposition. Also there's an /sqt/ up for just this reason.

Polite sage

>Doing thermodynamics problems
>One of the questions reads "A building is heated to 27 degrees C. How much heat per second could be supplied by an electric heater, with power input 20 kW?"
I'm tempted to just say 20kJ, but I'm awfully afraid that it's more complicated than that. I'm not looking for an answer, I'd just like to know whether or not it's as simple as it seems.

>>8442914

are quaternions just 3d imaginary numbers?

why is their 4 (ijk + a real number) and not 3 (one for each axis)?

>>8444105
the nice thing about quaternions (along with reals and complex numbers) is that you're able to do division

its a result of frobenius that these are the only finite-dimensional real algebras, there's just no way to do it in a 3-dimensional setting
https://en.wikipedia.org/wiki/Frobenius_theorem_(real_division_algebras)
https://en.wikipedia.org/wiki/Quaternion#History

In kinetic modular theory, can a single gas particle have a temperature?
assuming 1m^3 box , and velocity is constant.

on a side note does anyone know the proof of mean/average ? ( Im trying to see if you can take the average of a set containing only one item)

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>>8444654
Q2=-6Q1

How do I solve for the electric potential (voltage) on the central axis? Would I just add up 2 integrals of dq/r one for each charge density? How would I account the diferent sizes?

>>8444105
rotations in 3d space must be represented by a 4d object. Think of it as 3 values to represent the axis of rotation and one value for the angle. Quaternion components don't translate this way, but because they represent a rotation in 3D space, they still need to be 4-dimensional

>>8444903

By the superposition theorem, you know they add together. So you just take the integrals as you normally would but split them up by the charge density.

>>8444105
Because of the topological structure of the projective plane. Homogeneous coordinates have a multiplier(the real number)

I'm trying to find the maxima and minima of a function, and have come to sin(x) + 3.25((cos(x)^2 - (cos(x)^(5/2)) =0 and I'm having a hell of a time solving for x here. I was thinking of relating it back to cartesian coordinates, but does anyone have any other ideas?
I tried plugging it into wolfram and it told me x= 6.28318n, i.e. x = 2n pi for only integers; but I've found other points across my range (from 0 to pi) that work and give a non 0 values, so the max can't be 0.

>>8445420
Is that the function or the first derivative?

Are quaternion numbers less real than imaginary numbers? Is a quaternion:imaginary as imaginary:real? Like, when your dream has a dream?

why can't the surface area of a revolution be just the integral of the circumference formula with the radius being some arbitrary continuous functon?

volume of revolution works fine with the area formula, so, likewise, why can't the circumference work for the surface of a revolution?

for example
I have the curve sin(pi*x) to revolve around the x-axis from 0 to 1, but the surface area isn't four, its rather some irrational number 7.77939.. , wtf?

>>8445471
What I have there is the first derivative of the function

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Are there any websites that serve as viable hominin fossil databases?

I have a math exam tomorrow evening (general mathematics 2) that I'm a bit behind in terms of revision for. I have all day tomorrow free up until I have to go in for the exam. What is the best way to use my time effectively, should I just do what I normally do and work through past exam papers?

>>8445697
start right now
do pomodoro technique (get the app)

>>8442914
What are the latest research results about the P = NP problem?

>>8445706
Thanks. I can't really start right now as I was just doing some things before going to bed but I'll be sure to usei t tomorrow.

What is the 4th derivative of some X? I found an answer as 2/x^3, is this true and how is this kind of derivation called? Otherwise it would be 0 ofc, but this one is different, and how is that 0*x^{0-1} part jumped?

I want to get a subscription for a science journal, anyone got any recommendations?

>>8445936
Can't you just get them at your uni library or online ? Interesting papers don't always come from a single journal, that's why universities have subscriptions to dozens of them

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>>8445574
I don't know why it doesn't work. Probably because perimeter is a one dimensional thing.

>>8445936
Well usually people subscribe for thing in their fields or shit you are interested in. Asking for recommendations kinda ruins the whole purpose of it, doesn't it? There are science journals for everything. Probably there is a journal for mycopathologies that affect hands and another one for mycopathologies for feet etc

>>8442914
What is catnip, and what does it do to cats?

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Not sure if this belongs here

Why am I missing some dll files from my computer? How do I get them back? I'm trying to run a pirated game, but when I try it says I'm missing certain dll files.

Explain to me injectivity and surjectivity of a function as if I were a mentally retarded person

>>8446551
>>>/g/

>>8446551
[spoiler]just google the dll name, download it and put on the game directory[/spoiler] Just make sure you don't download dll.mp3.exe.notvirus

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quick sci, if im writing a personal statement or CV, and i have a publication getting ready to be submitted, how do i indicate this in said statement or CV?

like Anon, A. Formation of Meme Molecule complexes as delivery systems for other meme molecules. J. Dank Memes. (in preparation 2017)

or how? pic unrelated

>>8446579
thx bro
>>8446613
I found a website dllyes.com that has dll files but i just don't want to get screwed by viruses. Do you know of any legit websites good for dll files?

Say an exam has 3 topics. If I only care about passing, and not my grade, is it worth devoting all my attention to the two that I'm best at and just doing what I can on the other one during the exam? Or is it best to prepare for all 3 topics evenly?

The third degree Taylor polynomial for $ln(x)$ centered at 1 is $f(x)=(x-1)-\frac{(x-1)^2}{2}+\frac{(x-1)^3}{3}$. Now, $f(0.3)=-1.0593$ and $ln(0.3)=-1.2040$. $|ln(0.3)-f(0.3)|=0.145$. However, the error bound is supposed to be $\frac{(0.3-1)^4}{4}=0.06$.

The actual error is bigger than the bound?

>>8447311
The third degree Taylor polynomial for $ln(x)$ centered at 1 is [math]f(x)=(x-1)-\frac{(x-1)^2}{2}+\frac{(x-1)^3}{3}[/math]. Now, [math]f(0.3)=-1.0593[/math] and [math]ln(0.3)=-1.2040[/math]. [math]|ln(0.3)-f(0.3)|=0.145[/math]. However, the error bound is supposed to be [math]\frac{(0.3-1)^4}{4}=0.06[/math].

The actual error is bigger than the bound?

>>8447084
>all 3 topics evenly
this. most profs would rather have you understand 10% of every concept in the book than only know a few of them really well.

Retarded who knows nothing here.

I have a fear with black holes, I have no idea why I'm afraid.
I ask: Is it okay fear that one of them come to us? Seriously, I'm afraid.

>>8447316
why is (0.3-1)^4/4 your bound?

>>8442914

Anyone here know enough about astronomy to
say why this is BS that the media thinks is ET's?

Discovery of Peculiar Periodic Spectral Modulations in a Small Fraction of Solar-type Stars

Ermanno F. Borra and Eric Trottier

>>8446551
God is punishing you. Commandment #11 = no torrents, Noah knew this 1000 years ago. Repent!

>>8446624
It only goes on there if you've at least submitted it.

If you really need to tell someone about it, just tell them in the email or interview or whatever.

>>8447084
Impossible to answer. At the very least post the subject you are referring to. Also what level is this? Undergrad? You should really find the time to hit all 3 areas.

>>8447379
Undergraduate Physics. The topics are Electromagnetism, Diffraction/Scatter/Refraction/Dispersion (Atmospheric Optics), and Lenses/Mirrors etc, smaller scale optics.

>>8447339
I don't know if it's the professor or PhD students that mark exams. Would I be better off in terms of my overall mark to distribute my understanding evenly rather than focus on a couple of topics, in that case?

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What equations am I supposed to use?

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I'm trying to prove to somebody mathematically that theoretically Pokemon is inherently very resistant to power creep. To do this, I want a relatively accurate number of all possible Pokemon while keeping it within the same total base stat (the exact measurement of the Total Base Stat doesn't matter). While some combinations would be less effective than others, doing it this way means that there shouldn't be a need to create Pokemon with higher TBS, or a hard power creep.
There are 6 stats for each Pokemon, and for simplicity's sake I'm spreading it at Low=1, Medium=2, and High=3 for a TBS sum of 12. Is there an easy way to calculate all possible combinations in one equation? If so, how do I do it and how many combinations would there be? Full autism mode where Very Low=0 and Very High=4 could be included. Things like including combinations like HLHLHL or LHLHLH is tripping me up

>>8443103
W = J/t
1W = 1Js^-1

So the heater is rated at Q = 20000Js^-1.
Your kneejerk answer was right.

>>8444918
Not that guy but how would you do it? How would you represent one part being 1/4 or the circle and the other being 3/4?

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Anyone here who knows Python? I've been into it for a week and know the early basics pretty well now. I don't follow a course or anything but to test myself I've been looking at simple programs to make at my level

Pic related, I managed to make a simple palindrome checker but does anyone know the function body for pic related? Not the docstring

>>8448085
/g/'s better for these kind of questions

How is it that the moon is in line with the sun and can even block out the sun during a eclipse. Does not prove we are in a holographic program?

>>8447501

>undergraduate physics

easier than you think. your future classes will probably make you cry

>electromagnetism, diffraction/scatter/refraction/dispersion, lenses/mirrors

Seriously, just sit down and do all the homework problems. It will take for fucking ever but you will pass the exam so easily. At the very least practice writing down the formulas and proper units. Understand how to change to proper units. 99% of the test is knowing the formula, knowing how to change units of said formula, and 1% is actually doing the calculation correctly. When you start the exam you should be able to write down all the pertinent formulas for a problem immediately.

The professors don't expect you to actually know proper physics at the end. You are learning the equivalent of 2 + 2 in physics when future classes will be like calculus.

Why is the integral of x^2 x^3/3 the integral of x^4 x^5/5 etc? I'm not exactly asking for the answer but possibly the name of the theorem or a link to something that i can find the answer with.

>>8448213
https://en.wikipedia.org/wiki/Power_rule

>>8448129
Ok, thank you. This is second year stuff, I don't know if that makes any difference.

>>8448217
Thank you

Chemistry question.

I took some 6mol HCl, copper wire and water and mixed it all in a bowl until it turned bright green. I think its Cu(ii)Cl2.
Then I cleaned a square, steel pipe with some HCl to get rid of the rust.
I placed one end of the steel in the solution. I then added a 2A car battery starter terminal to one end of the pipe and the other terminal into the water.

The steel became plated with copper, but only around the corner of the pipe.

Why is that and what can I do to completely plate the pipe?

I dont have any pics, i was half drunk in my dads garage proving a point.

Sets and number theory is killing me off. I understand what I have to do and prove clearly but I don't know how to write down my answer.

e.g. when proving a relation is equivalence I feel like I'm stuttering in my steps when proving the properties and then I have a messy looking proof. Say I want to show its transitive property I just reach a stumbling block and have to keep scratching and retrying manipulations until I get it-and it feels so unnatural and wrong

Tldr How do I properly visualise a proof to write it down and have the reader understand it clearly?

>e.g. when proving a relation is equivalence I feel like I'm stuttering in my steps when proving the properties and then I have a messy looking proof. Say I want to show its transitive property I just reach a stumbling block and have to keep scratching and retrying manipulations until I get it-and it feels so unnatural and wrong
practice more of them

>Tldr How do I properly visualise a proof to write it down and have the reader understand it clearly?
you don't just 'visualize' a proof, you find out what you need to show and then work through the steps. write your proof after getting rid of unnecessary/complicated steps, show it to someone and see if they understand it

is there a particular transitivity argument you find difficult?

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Hello /sci/, how would I prove, i a mathematically way, the following situation:
If I draw a number of n circles onto a plane, which splits said plane into different areas - I could paint every area either black or white, without ever two areas of the same color touching.

>>8448364
>paint two areas apart from eachother black
>leave all others white
What is the problem?

What's it called again when someone cites an entire bookwork as evidence against your claim in a discussion, and he expects you to read it all so you basically do the job for him? I think of spoonfeeding but that's not the term I'm looking for.

>>8448369
not an argument

there is no statement that can be rebutted by [book title]

there might be a statement in the book but just citing the book doesn't mean anything

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>>8442914
What is the most concise way to convince flat-earthers that Earth isnt flat?

>>8448548
There is no way. They'll just rationalize and invent something else. Just like /pol/tards

>>8448573
This. As a general rule, you can't reason someone out of a position they didn't reason themselves into in the first place.

Why is the maximum reaction rate of a noncompetitive inhibitor is lower than the max reaction rate of a competitive inhibitor?

>>8448364
What if I just draw two disjoint circles on the plane ? I get three areas and there are bound to be two of the same color touching if I paint them in black and white right ? Or am I not understanding the problem statement ?

>>8448548
convince them that their arguments actually turned you into a flat earther, they might be so horrified that they break character and admit they were trolling.

>>8447636
Is the only way to just count each individual combination?

Can I get into engineering with a Bachelor's in Math. If I get a BMath, what should I get as my Master's Degree?

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Im taking an algebra course in a community college, am I already fucked as far as engineering degrees go?

>>8449225
>>8449225
>am I already fucked as far as engineering degrees go?
No. But you better have one hell of a work ethic.

>>8449263
what makes you say that?

>>8449282
Was in your same position last year, now I'm transferred to a normal Uni, the catchup time is enormous when you come in without the mathematics background. You will have to take a bunch of math all at once right going in, and the courseload can be really overwhelming. You have to reteach yourself a lot of mathematics on your own on the fly to keep up.

>>8449193
You can't get a professional engineering license, but you can get some engineering jobs (the only career ceiling being you can't commission anything without a professional engineer's signature, do consulting etc.).

>what should I get as my Master's Degree?
If you're gonna do grad-school anyway getting an engineering bachelors will be worth to you then do math postgrad, not the other way around. If you can get into an accredited eng masters programme do that, but schools were you don't need an accredited b engineering degree are usually just applied science research degrees that aren't accredited.

Anyone here have experience with RobotStudio and programming in RAPID?

Is /sci/ still an existential hole full of malice?

>>8449465
That's a bit generous, but on a good day it approaches that.

A 1.9kg mass, Ma, and a 4.0kg mass, Mb, are connected to a lightweight cord that passes over a frictionless pulley, what is the acceleration of Ma if gravity acts in the negative direction

>>8449499
You need to draw the free body diagram for both cases. Since they're on the same chord, you can solve it using their relationship of tension T

Is homogeneous (like in DE) pronounced ho-mo-jee-knee-us, ho-mo-jee-nus, or hom-awe-jen-us?

>>8449513
the first one

>>8448618
you said disjoint circles so just colour both circles black and their complement white

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how do you solve this?

>>8449633
solve what? a sum isn't a question

>>8449637
how do you simplify it then?

>>8449622
Shit I *was* tired.

>>8449643
what is c?

>>8449648
c is real

>>8449651
https://en.wikipedia.org/wiki/Geometric_series

>>8449633
Write the sine as a sum of exponentials, expand

>>8449654
no brainlet, if c is an odd integer then the sum diverges

otherwise it's equal to 1/(1-sin(pi*c/2))

Could someone help me with a proof? The situation is this:

>f(x) is a polynomial of degree n, p is a prime
>a is a root of f(x) mod p, so f(x) = (x-a)q(x) + c, where c is divisible by p and the degree of q(x) is n-1
>Not all of the coefficients of f(x) are divisible by p

Knowing all of this, how do I prove that not all coefficients of q(x) are divisible by p? Apparently it's a quick and easy proof but I'm dumb and need help.

Any Civil Engineers here?

Turns out our senior "capstone" project has no creativity whatsoever, it's wholly assignment-based for the entire class. Kinda disappointed.

Anyone know of any ideas for self-projects I can do for fun and to boost the resume? Already done some ASCE stuff.

>>8449687
Well what are the coefficients of f ?
[math]f_0 = c - a q_0[/math] and
[math]f_{i+1} = q_i - a q_{i+1}[/math]
If all the coefficients of q were divisible by p, then all the coefficients of f would also be divisible by p.

>>8449696
Welp, that seems to be the case. Thanks a lot anon.

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I'm in a Circuit 1 class and wanna know what kind of circuits could be built using op amps, LEDs, resistors, battery, and capacitors.

I'm just not sure what op amps can and can't do, was wondering if I could create a circuit with multiple LEDs oscillation

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How to find out area of the grey zector?
I think that : S(of the sector)=(Q2-Q1)/360 * pi(r1^2-r2^2)
Am I right?

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I've got a stupid physics question that I just can't figure out. If an antelope is running at 7m/s at the moment it passes a lion, and the lion chases, accelerating at a rate of 5m/s, how long does it take the lion to catch up to the antelope?

Aren't I supposed to use the horizontal distance formula or something?

>>8449855
die in hell scum.

>>8449855
kill youreself brainlet

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>>8449870

>>8449855
Just plug everything you know about the animals into [math] s(t) = \frac{1}{2} a_0 t^2 + v_0 t + s_0 [/math] and then check when both functions are equal.

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How can Mars be a dessert planet if its FURTHER from the Sun than Earth is?

Astrologers BTFO!

>>8449887
it's more of an arid planet, that is covered with dust and sand maybe, because there is little water on the planet.

Deserts do not have to be hot.

Here's one that'll probably get skipped since /sci/ is a bunch of high schoolers.

Why do the Chapman–Kolmogorov equations seem to not care about the fact that matrix multiplication does not commute?

>>8449973
why dont you put some effort into your question and give some relation that unintuitively seems to ignore this commuting?

>>8447347
Probably not, but phobias generally are irrational, such as fear of spiders, water or clowns. I've felt what you felt but no humanity isn't going to be eaten by a black hole

>>8449717
you can make a signal derivator/integrator

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>>8442914
You see how small my toolbar is

How to i fix it to be its original large size?

I dont know if my phone's gonna flip the pic or not

>>8447347
I suggest checking out Space Engine
http://en.spaceengine.org/

The reason people are afraid of this kind of thing is they don't fully appreciate just how fucking far apart everything is. A black hole isn't going to get anywhere near us in anybody's lifetime.

>>8450082
Why don't you just learn the keyboard shortcuts, brainlet?

what path should I take to understand with decent rigour Stokes generalised theorem? and basic properties of manifolds and so on? any textbooks?
i have a basic understanding of metric and topological spaces

What does [math]§^n[/math] refer to in mathematics? It's listed in my notes as an example of a path connected space, but I don't know what it is.

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>>8450327
i assume thats supposed to be [math] S^n [/math] which is the n-sphere
https://en.wikipedia.org/wiki/N-sphere

>>8450334
No, we've used [math]\mathbb{S}^n[/math] to refer to the n-sphere in this topology class before. I suppose it could be a typo, but I doubt the professor mistook § for S somehow. It's listed as a path connected space in the notes she posts online, but I don't recall going over it on the day this topic was discussed.

>>8450341
if they're latexed notes it's a very possible typo, otherwise i've never seen anything use that symbol aside from a section number

>>8450346
Alright. Thank you.

>>8445914
The derivative of x is 1, and the derivative of 1 is 0. If you start up again with x^-1, you can keep taking derivatives using your formula, but it doesn't work to "cross over".

>>8446637
As a dll it can't cause any harm until you run the exe that uses it. Simply download the dll and then scan it for viruses. I've never had a virus from a dll and I download from those random dll sites all the time.

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What's the quickest and simple way to determine if a system of linear equation (n x n) has a unique solution or not?

I know there are a lot of ways to determine it but I don't know which one would be the fastest algorithm to implement it

Dumb question regarding super position and dependent sources. Do you just treat them as you would an independent source, with a dependent voltage source being a short and a dependent current source being treated as if it were open but just ignore them when reactivating?

>>8450414
>What's the quickest and simple way to determine if a system of linear equation (n x n) has a unique solution or not?

If det [A] != 0, there is a unique solution

>>8450466
But isn't calculating the determinant of a matrix a very lengthy process? Isn't there a better way to do it?

>>8450469
If you can put it into row echelon form with no non-zero pivots, it's also invertible and has a unique solution.

I don't calculate squat anymore by hand. Just throw it in matlab or punch it into your calculator.

You can also look through all the other subitems in the invertibility theorem, and see if one of them looks easier to you.

>>8446551
buy the game

So everyone in my circuit analysis class uses chegg or something to get their answers for homework and I'm left alone not being able to ace my homework. I keep getting rekt for it. Should I get chegg? I mean, I have wolframalpha, but how can I do circuit analysis with that?

The professor is not that nice and my fucking classmate is a faggot, even though I gave him a pdf of the book and let him share my lab tools he was like "I paid for my chegg and I don't want you leeching off my money"

I'm trying my best to do the homework from looking at notes and book examples, but I keep getting one digit scores on my homework.

My question is, how can I use wolfram to get step by step solutions of circuit problems?

>>8450478
I also am not going to calculate by hand. I'm trying to do a very simple equation solver program but when I capture a system of equations I would like to know if it has a unique solution or not and I'm trying to figure out the fastest algorithm to do it.

Since in that same program I'm also trying to implement other things, I won't always would like to know the solution of the system, I just want the fastest way without looking at any other benefits like for example trying to find the inverse matrix and if I do, I know it has a unique solution and can multiply it by the vector b to get the solution.

Somebody explain subspaces and span (linear algebra) to me like I'm a non-math major idiot.

Seriously struggling to conceptualize what the fuck is going on here.

>>8450497
What are you struggling to conceptualize, exactly?

>>8450536
Well, here is a definition given in my linear algebra book for a subspace:

A nonempty subset V of vectors in Rn is called a subspace
of Rn if V = SPAN(S) for some nonempty finite set of vectors S in Rn. (In
other words, subspace is just another name for SPAN(S).) We say that the set
S spans V or is a spanning set for V .

I sort of understand what a span is, and what a subspace is (closure and all that), but I'm confused as to how subspace is the span(S).

>>8450558
Ok, I see how that definition is a confusing way of putting things. It's kinda backwards from how you would normally think of it.
So, let's say you have a set of vectors, S. Span(S) is the set of all possible linear combinations of those vectors. Now, hopefully you can see that Span(S) is a vector space (check it against the vector space axioms, if you need).
Now, say you have a set of vectors, V, which is a subset of R^n (or whatever vector space). If you can find a set of vectors, S, such that Span(S) = V (ie. S 'spans' V), then you know that V must be a subspace.

>>8450586
In other words, V = Span(S) means that the set of all linear combinations of the vectors in S is exactly equal to V.

>>8450586
thank you, that clears it up

>>8450490
check if you can get multisim or similar program free through your uni, I use it to check all my hw problems

>>8450607
I think we have some type of PSPICE, but I want something that shows step by step work so I can see what's going on. That's a good idea too. Though, I use that circuit simulator website falstad.com/circuit but I don't know if it has similar results like PSPICE

>>8450614
that site doesn't work well on my phone and I haven't used pspice, only in 1st circuits class so idk mane. I think trying out pspice or multisim now would be useful later on though

Learned L'Hopital's rule in class today, but the professor didn't make something very clear.

Does this mean if I need to take the derivative of a quotient of functions, say f(x) / g(x), for a specific x value, then the derivative equals f'(x) / g'(x), but only if f (x) / g(x) is indeterminate, and I can use this as a shortcut around the quotient rule in this case?

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>>8450683
FUCK NO

the derivative of a quotient is always given by the quotient rule.

L'hopitals rule is the following:

If I want to find the LIMIT [math] \lim_{x \rightarrow c} \frac{f(x)}{g(x)} [/math] but the limit is indeterminate, ie [math] \lim_{x \rightarrow c} f(x)=g(x)=0 [/math] or [math] \lim_{x \rightarrow c} f(x)=g(x)=\infty [/math] THEN [math] \lim_{x \rightarrow c} \frac{f(x)}{g(x)} = \lim_{x \rightarrow c} \frac{f^'(x)}{g^'(x)} [/math]

>>8450724
[math] \lim_{x \rightarrow c} \frac{f(x)}{g(x)} = \lim_{x \rightarrow c} \frac{f^'(x)}{g^'(x)} [/math]

also it's supposed to read [math] \lim_{x \rightarrow c} f(x)= \lim_{x \rightarrow c} g(x) = 0 [/math] ect

>>8450729
oh for fucks sake

[math]\lim_{x \rightarrow c} \frac{f(x)}{g(x)} = \lim_{x \rightarrow c} \frac{f'(x)}{g'(x)} [/math]

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How do i do this with a varying frequency?

>>8449990
>why dont you put some effort into your question and give some relation that unintuitively seems to ignore this commuting?
I'm well aware that there's plenty of things you can do with matrices that ignores commuting. It's specifically the Chapman–Kolmogorov equations that confuse me in terms of why they don't care about commuting.

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Can someone explain me why some components are crossed out or why E parallel to x and B parallel to y implies that.

>>8450683
Take the derivatives separately.

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So I'm on problem 5b here, and I'm stuck. I feel like I have a very strong misunderstanding of the mathematical mechanics I need to perform here.

I solved [math]det(A-\lambda I)=0[/math] as [math](1-\lambda)^3=0[/math] for a real repeated eigenvalue of [math]\lambda=1[/math] of multiplicity three. Then I solved [math](A-\lambda I)V_1=0[/math] for [math]V_1[/math] by setting up an augmented matrix with [math]A[/math] and the zero vector to get [math]V_1=[0~1~1]^T[/math].

Now, I check wolfram (http://www.wolframalpha.com/widgets/view.jsp?id=9aa01caf50c9307e9dabe159c9068c41) and it says that there is one eigenvalue,[math]\lambda=1[/math], but that it is only of multiplicity 2, and that there are somehow two eigenvectors, [math]V_1=[0
~1~0]^T[/math] and [math]V_2=[0~0~1]^T[/math].

I'm not sure how exactly that's supposed to be calculated. I see that the two eigenvectors that wolfram calculated can be formed by separating the one I have into two different ones, but I'm not sure why that's so. On top of that, I could use some clarification as to why we only need two eigenvectors here when we would need three to construct a transformation matrix.

>>8450896
Whoops, [math]V_2[/math] is showing as [math][1~0~0][/math], does this have something to do with the fact that [math]A-\lambda I[/math] gives x and y as free variables?

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>>8442914
Can you stop renaming the /sqt/? It makes it hard to find, and /qtddtot/ is from /fit/ or something

Anyone knows what theorem is this assertion based on?

[eqn]
(\bf{y} - \bf{X}\bf{\theta})^T(\bf{y} - \bf{X}\bf{\theta}) \\
= (\bf{y}^T\bf{u} - \bf{y}^T\bf{X}\bf{\theta} - \bf{\theta}^T\bf{X}^T\bf{y} + \bf{\theta}^T\bf{X}^T\bf{X}\bf{\theta}
[/eqn]

The 2 terms in the middle of the second equation... How come my professor wrote them as [math]-2\bf{y}^T\bf{X}\bf{\theta}[/math]? Are they not the transpose of each other? Sine when [math]-\bf{X} - \bf{X}^T = -2\bf{X}[/math]? Is this true only when the matrices are symmetric, so that means that the product of matrices above was symmetric for some reason?

>>8448085
So are you in Andrew's class? Did you fuck up the midterm?

How do you calculate
[eqn]
\frac{\partial \bf{\theta}^T\bf{X}^T\bf{X}\bf{\theta}}{\partial \bf{\theta}}
[/eqn]

I thought it's something like [math]\bf{\theta}^T\bf{X}^T\bf{X}[/math] but I feel like it's[math]2\bf{\theta}^T\bf{X}^T\bf{X}[/math], but not sure where the [math]2[/math] comes from. Anyone?

Need help with graphing linear inequalities. Ok, if I have xy = 0. Is it only the origin, any point or only x-y axis?

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Pls respond

>>8451103
No, the bottom one is a partial derivative. Aren't the same when there is more than one variable

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>>8451113
Is this correct then?

>>8451166
Yeah bruv that's right

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How to find out area of the grey zector?
I think that : S(of the sector)=(Q2-Q1)/360 * pi(r1^2-r2^2)
Am I right?

>>8451192
remove the small area from the big one not the oposite

REALLY stupid question incoming:

Basic Order of operations shit...

I'm doing basic matrix multiplication and am just curious about the correct order (C, D, E & F are given but I doubt it's important)

(CD)^2 - 4EF^2

The correct order is to square CD, then square F, multiple F by E and then multiply the resulting answer by -4? I feel retarded..

>>8442923
I assumed R2=4 ohms because you didnt tell us ya dingus. May I ask you where you were asked this question? Uni?
Using that you get I1 = -0.5A, I2 = 1A, I3 = -0.75A.
Use superpussyition principle ya dum dum

>>8451228
*multiply E by F^2
matrix multiplication doesn't commute.
scaling does so -4 factor can move all over the place

>>8449776
Should be r2^2 - r1^2, but yea, assuming "Q" is given in degrees.

I have a three digits number xyz
z = y + 4
x = y - 4
If I rearranged the numbers in xyz to zyx,
zyx = xyz + 792
Find xyz.

I know the answer is 159, but I just can't get the right answer. No matter what I do I always get 0 = 0.

What I tried to do:
100z + 10y + x = 100x + 10y + z + 792
99z - 99x = 792
99(y+4) - 99(y-4) = 792
99y + 396 - 99y + 396 = 792
0 = 0

It makes sense why I get that, because if I put the answer in I just do 951 = 159 + 792, which is basically the same as 0 = 0, but I don't understand what I should do differently.
Help?

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Can protons or whole atoms exhibit quantum mechanical phenomena?

>>8451211
Oh, yeah. r2^2-r1^2
With with correction, problem would be solved?

>>8451249
Yes. Look into cold atomic gas realizations of Bose-Einstein condensates. Even more complex, I think the double slit experiment has been performed with C60 buckyballs.

>>8451236
Thanks

>>8451254
Yes. Or you could integrate two parametric circles from one angle to the other and subtract the smaller from the larger

>>8442914
ok so i think i might actually be retarded. how would i go about solving somthing of the form a = cos(xy)/sin(xz) for x.

>>8448085
Do you mean the second one?
Just iterate from the given index outwards until the elements accessed are not equal, then return the string slice between those indices.
I.E, start with the element at i, then check if arr[i+1]==arr[i-1] then if arr[i+2]==arr[i-2] and so on until you find an inequality. When an inequality is found, return the string between the last equal indices. This should just return the single element at the index itself if there is no palindrome.
You shouldn't need me to write the syntax out.

>>8451249
https://www.youtube.com/watch?v=pktWhH6m_DM

>>8447339
It's better to practice a kick a thousand times than to practice a thousand kicks once

>>8449717
Yes. You can build an oscillator using op-amps.
I'd build a circuit that solves a particular class of differential equations where you can set the constants with variable resistors and capacitors and display the results in binary on LEDs using comparators. ur profs will b v imprsossed

>>8448085
ispalindrome = lambda l: l == l.reverse()

>>8448548
go to a beach and lay flat on your back watch the sun set. then stand up and watch it happen again.

flat earther BTFO

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>>8451341
Nuc= Kernel of something.

My teacher is a german dude that has a thick accent, I can't understand anything and his material is 10x worse.

Imagine both of these are linear transformations from R2 to R3, are they possible transformations? (Rank-nullity theorem). I think they are, both images have dimension of 1 and so the kernels.

>>8451343
Fug didn't meant to quote.

>>8451246
Wait, maybe I just need to check values 0 to 9 for y and see if the equality is true?

>>8451023
Please.

>>8450163
guise plox

Question: Demonstrate than sqrt(6) is an irrational and deduce thant sqrt(2) + sqrt(3) + sqrt(6) is irrational too.

I know how demonstrate thant sqrt(6) is irrational but i don't how deduce than sqrt(2) + sqrt(3) + sqrt(6) is too.

Someone can help me please ?

>>8451023
look at the graph of xy=1
then at the graph of xy=0.5
then xy =0.1 and so on
that is not an inequality btw

a/bc/g = what with one "/" ?

>>8451376
You mean like fractions?
a/bc/g = a/bc * 1/g = a/bcg

>>8451385
yes, ok thanks, i found the same but seemed me weird

>>8451359
A still need to "paint" the part where in the coordinates this equality is true. Since it showed during the inequality part of the book, I called it the same.

>>8451355
try taking sq6+sq3+sq2 and assuming it is rational. then cube it.
it's cube is supposedly rational. try to prove that it isn't while assuming that the sum of three sqroots is rational

>>8450591
>>8450497
A subspace is simply a subset that is also a space. Being a space is equivalent to being the span for some set of vectors.

>>8451023
it is the two axis

if x=0 then y can be anything, and vise versa

>>8450962
>>8450956
>>8450946
bump

>>8451601
what is 1.151?

I am learning calculus of variations and was trying to apply it to structures, but I have no Idea what I should be trying to minimize. None of the answers I got seemed correct so far.

Suppose a simply supported beam of length L with supports on its extremities and under a distributed load w. What is the shape of the beam that makes it the most "resistant" possible?

What is the function F of the euler-lagrange equation?

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>>8442914
How would I go about this? I'm pretty lost because I don't really understand the notation very well. I get that it is the sum from x to x^2 for that function, but where does t factor in?

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>>8451628
It's pic related, but it sounsd like they base their conclusion solely on the fact that the equation is quadratic in a variable.

I am sorry to be such a dumb, but:

Evaluating integrals by u-substitution. I can memorize the steps to do it, but really intuitively understanding all of the details of what I'm doing is too much for my poor babby brain to handle. Even Khan Academy isn't quite doing it for me.

Anyone know of any good videos or guides that explain it thoroughly from the ground up?

hey guys just need a quick refresher: two sqrts of three is equivalent to sqrt(x^3). Am I correct here?

>>8451710
Newp. It's equal to sqrt(2^2*3), or sqrt(12)

>>8451700
quadratics have exactly one critical point and since that quadratic is concave up that point is a global minimum

>>8451709
The proof for the substitution rule is so simple I'm not sure if any intuition of the kind you're looking for is really even that applicable. The proof is very easy to follow and basically just uses the fundamental theorem of calculus and the product rule.
It's just a way of finding an equivalent integral to solve that's mechanically easier.
t. non-brainlet

>>8451697
Help

>>8451697
It is an integral from x to x^2. You solve the integral of t, apply the limits of integration, differentiate with respect to x, and put x=6.

>>8451733
What class is this for and for what institution?

>>8451103
it can
if x is a single variable function of t.
bottom is a partial derivative

>>8451166
im not gonna read that shit. tilt it or put it in wolfram.

>>8451734
I'm not that good with the terminology just yet.

So, by solving for the integral I get the anti derivative.

I'm not so sure what you mean by apply the limits of integration

And then differentiating it with respect to x, doesn't that just take me back to the original function?


What I'm thinking is: When you say apply the limits of integration, I sub in x^2 for t, and then differentiate? And then sub x = 6?

>>8451741
It's my first year calc class in uni. Sorry if it's a bit easy, I missed the two lectures where they did integration and am trying to catch up.

>>8451746
Also, McMaster Uni

>>8451729
Okay, badly written question. Hard to put this into words. I get what it does and why. What's throwing me is trying to visualize how the area under f(x) over one interval can be equal to the area of f(u) over a different interval, once the interval is adjusted in terms of HOLY SHIT I JUST GOT IT

>>8451744
You solve the integral for t, then substitute t=x^2 and subtract from t=x.

What branch of math will teach me how to maximise a function with respect to the sum of its variables? Example: 0.25x * ( 1.15 + .05y ) = highest possible ; x + y = lowest possible

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How do I go about solving the resulting equations from setting [math]\textbf{v}(x, y) = \nabla F(x,y)[/math]?

I have [math]\frac{\partial F}{\partial x} = xf(r)[/math] as the first and I'm not sure how to integrate it.

I'm trying to prove the inequality:

1 - (1/2)x^2 <= cos(x), for x>=0.

Since this is for an exercise in the Mean Value Theorem section, i'm pretty sure I'm supposed to use it. Here is what i have so far:

define f(x) - cos(x), g(x) = 1 - (1/2)x^2. Then for all intervals [0, x] f and g are continuous, and for all intervals (0, x), f and g are differentiable. Thus f'(x) = -sin(x) and g'(x) = -x. By the MVT we have there exists c1 in (0,x) such that

f'(c1) = f(x) - f(0) / (x-0) = (cos(x) - 1) / x,

and similarly there exists c2 in (0,x) such that

g'(c2) = -x.

I'm not quite sure where to go from here so any advice would be most appreciated

>>8451785
Ah how could i forget: the hint in the back of the book says to use the "racetrack principle", which says if f, g are differentiable on (a,b), with f(c) = g(c) for some c in (a,b), and if f'(x) <= g'(x) for all x in [c,b), then f(x) <= g(x) for all x in [c,b).

Okay so now to use this i need to check the conditions: it is clear that f and g are differentiable on (0,x), but for what c are f'(x) = g'(x).. I will think about this more and return

>>8451769
> Example: 0.25x * ( 1.15 + .05y ) = highest possible ; x + y = lowest possible
Meaningless question. Neither expression has either a maximum or a minimum.

Optimisation requires either that the objective function has extrema (or at least local extrema), or the domain is bounded (which effectively means that redefining the function in terms of a parameterisation of the bounding surface results in a function with extrema).

wtf is the cartesian equation of the polar curve
r = 3sec(theta)

>>8451769
literally implicit derivation

>>8451805
x=r*cos(theta) = 3sec(theta)*cos(theta) = 3
y=r*sin(theta) = 3sec(theta)*sin(theta) = 3*tan(theta)

IOW, it's the vertical line x=3.

>>8451795
> for what c are f'(x) = g'(x)
Read it again. You're looking for f(c)=g(c) (hint: c=0), not f'(c)=g'(c) (which is also true at c=0, but that's irrelevant).

>>8451799
In this particular case, I want both x and y to be between 1 and 20 and their sum to be under 41, and I'm sure there's some sort of graph that could show me the solution in less time than it takes to fill in matrices.

>>8451811
Exactly what I'm looking for.

>>8451829
y has to be in terms of x, not theta

Someone please explain to me how you differentiate log(-1/x) with respect to x.

>>8451829
fuck, im so autistic, now I realize that for all inputs to this parametric equation, x will always be 3 meanig its a vertical line

>>8451862
d/dx [ln f(x)] = f'(x) / f(x)

>>8451866
d/dx ln(x) = 1/x
d/dx ln(-x) = 1/x

d/dx ln(1/x) = -1/x
d/dx ln(-1/x) = -1/x

Fucking took me a while to realise where the the 3rd minus is coming from.... Cheers

what exactly are irrational numbers (inb4 decimals that never end)
why can there be a finite surface area to the revolutions of some infinite curves

>>8451889
irrational numbers are anything that aren't a ratio a/b of integers

so like sqrt(2) [in fact sqrt(n) for any non-square n], pi, e

A chemical reaction A + B -> C requires 50kJ of energy per every mole of product C. This energy has to be delivered by exactly one mole of photons. What is the wavelength of light that must be used to carry out this reaction?

>>8451841
> In this particular case, I want both x and y to be between 1 and 20 and their sum to be under 41

So it's bounded. In which case, the maximum value of 0.25x * ( 1.15 + .05y ) occurs when x=20 and y=20. The minimum value of x+y occurs when x=1 and y=1.

>>8452083
This was a bad example since you get the most "bang per buck" by first raising x to 20, then raising y. Usually the path follows more of a curve that requires alternating which to raise at each step.

>>8452109
Most optimisation techniques change all variables simultaneously, i.e. finding the gradient vector then moving along it.

But the point remains: given two multivariate functions (e.g. f(x)=a*x*(c+b*y) and g(x)=x+y), you can maximise (or minimise) one or the other. But it's not meaningful to ask "how do I maximise one AND minimise the other".

If you have multiple "desirable" objectives, you just have to cook up an objective function which takes all of them into account, e.g. a weighted average or a ratio or whatever. Then you have something which you can optimise.

>>8451833
Most appreciated anon

>>8452136
I get what you're saying now.
Looks like the sticky is short on linear programming, but just knowing there's a formal jargon for this is already a huge help.

I want to be a brain in a jar.
What do I study?

>>8450962
>>8450956
bump

>>8452047
Just convert kJ in eV and then use the
E=h*c/λ
Where h is the Plank costant and c is the speed of light. Obviously you solve it for λ.
Pay attention to the units!

How demonstrate than -|x| =< x <= |x| ? for x real
Please.

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Can someone explain to me how my professor found the centroid of this shape? I jotted it down real quick in class and going back over it, I have no clue what he did. When I use the classic x(bar)=sum of x*A/Atot, I get a different answer

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>>8453126
This one as well, wtf he doing

>>8445420
>>8445582
This is just me spitballing it, but you could try using a substitution like g(x)=cos^2(x) and then factor that out of the parenthetical expression and then use trig properties to try and combine terms.

So could someone help me.
http://4chan-science.wikia.com/wiki/Mathematics
This has a good recommendation books and whatnot, but what is the right sequence in learning mathematics? Feels like learning Advanced Calculus before Algebra Linear too much, I don't think Algebra Linear needs that much of Calculus. What is the better way to approach mathematics past high school?

>>8453281
linear algebra requires no calculus aside from if you look at some very specific cases of vector spaces (continuous functions, integrable functions) and linear transformations (differentiation, integration)

single variable calculus and linear algebra can be learned separately, but advanced calculus (assuming you mean vector/higher-dimensional calculus) requires linear algebra

>>8445420
Can you post the original function, please. Maybe you made a mistake in differentiating.

I get updates from my university as a math alumni ( bachelors ) and they had a section on grants faculty got. There was a topologist in the department who got $250,000 over three years. Considering he's a pure mathematician who doesn't need any special equipment or time access to something expensive ( like a telescope ), where the hell is all that money going to go? As far as I know he's just goona be sitting in his office with journals and books. Post docs might as well be indentured servants. Can someone who knows about grant funding maybe fill me in on where how the department is going to doll out this money?

>>8453447
going to conferences
flying people in to your seminar
computational power
funding grad students
living comfy while doing research

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I intergrate and get -k/2 (e^z^2)=1

I equate to one because it's probabilty density function(Kek I dno)

How I find value for K

Wat do?

>>8453471
>-k/2 (e^z^2)=1
how?

>>8453281
>What is the better way to approach mathematics past high school?
Kind of depends on where your interests lie. If you want to do engineering or physics, get some linear algebra under your belt as soon as you can.

>>8453481
Engineering and also pure mathematics. I just want to get enough mathematics as I would if I went to college.

I guess I missed statistics 101, maybe you guys can help me out?

I'm going to use an example from http://www.cdc.gov/cancer/lung/basic_info/risk_factors.htm. My choice of example is arbitrary and is of no importance (I'm not that guy that keeps posting about how good smoking is for you).

>People who smoke cigarettes are 15 to 30 times more likely to get lung cancer or die from lung cancer than people who do not smoke.

1 How accurate is this statement from a statistical viewpoint? First of all, can you really say that an arbitrarily selected smoking individual is 15 to 30 times more likely to develop lung cancer as compared to an arbitrarily selected nonsmoking individual or the entire set of nonsmoking individuals? I thought you could not apply statistics to make statements about individuals, so does this all boil down to poor use of words in vernacular texts?

2. Does statistics not differentiate between probabilities and amounts? By that I mean, is there a distinction between having a 20 percent chance of x and 20 % of the outcomes being x?

3. I'm assuming that the most correct (and thus autistic) way of rewriting the greentext is "the set of people who smoke cigarettes and get lung cancer is 15 to 30 times larger than the set of people who don't smoke and get lung cancer", is this correct?

Thanks in advance.

Taylor expansion: I understand why it approximates a function around the point for which we're expanding. But I am still not confident with Taylor expansion due to the following questions:

1. Why we allow ourself to neglect higher order terms?

2. To me it always seems arbitrary when some textbook says "neglecting terms of order 3 or higher".. Exactly how do I chose what terms to neglect?

3. Why do some textbooks use [math]=[/math] instead of [math]\sim[/math] after some term of a function [f] has been approximated with Taylor expansion (is it not an approximation?)?

4. In textbooks authors typically write "Expanding [math]f[/math] around [math]x*[/math], we get that [...]" without stating why a Taylor expansion is the reasonable choice of action. How should I recognize when solving a problem that Taylor expansion is a necessary or reasonable course of action?

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>>8453476
Wat now. How I get K

>>8453587
why do you have no bounds on your integral?

>>8453591
I don't know what the bounds are...

>>8453559
>Why we allow ourself to neglect higher order terms?
>To me it always seems arbitrary when some textbook says "neglecting terms of order 3 or higher".. Exactly how do I chose what terms to neglect?
One of the applications of Taylor expansions is numerical approximations of functions. You will usually just want to evaluate a function up to a certain degree of accuracy, in which case you would just use a certain number of terms of the Taylor expansion. How many terms you choose to use depends on how accurate you want to get.

Keep in mind, of course, that the *limit* as the number of terms in a Taylor expansion approaches infinity IS precisely the value of the function at that point. But this is useless for computation purposes.

Why do some textbooks use == instead of ∼∼ after some term of a function [f] has been approximated with Taylor expansion (is it not an approximation?)?
Might just be a crappy textbook. But again keep in mind that a Taylor expansion with an infinite number of terms is exactly equal to the function.

>In textbooks authors typically write "Expanding ff around x∗x∗, we get that [...]" without stating why a Taylor expansion is the reasonable choice of action. How should I recognize when solving a problem that Taylor expansion is a necessary or reasonable course of action?
It depends on the problem, but sometimes it is easier to integrate or take the derivative of a function's Taylor expansion than to integrate or take the derivative of the function directly. For example, how do we know that the derivative of e^x is e^x? One way of proving this is to replace e^x with it's Taylor expansion and then take the derivative of that. Since the Taylor expansion is a polynomial and we know how to take derivatives of polynomials (power rule), we can do this. You will find that taking this derivative gets you back the same Taylor expansion!

>>8453595
look what interval the probability distribution is defined by that function on...

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>>8453598
>Since the Taylor expansion is a polynomial

>>8453599
Z>0

So the bound is...?

My guess is infinity and zero.

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>>8453609
well done!

>>8453604
The taylor expansion of e^x is indeed a polynomial, brainlet.

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>>8453612
>infinite series are polynomials

>>8453611
I get why infinity but why include zero when z>0. How did the zero sneak in?

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>>8453616
the function is 0 at z=0 anyway, it doesn't contribute anything to the integral

>>8453559
On (0,1), the more times you multiply x by itself the smaller it becomes. This is saying, roughly, that the higher order terms are small enough to be ignored for the current purpose. You can actually generate explicit formulas and approximations for the error in neglecting the remaining terms. Say you wanted a polynomial within .001 of the true function on (a,b). You can easily add terms until the error is acceptable.

Why would you want to use a taylor expansion? First, polynomials are far more "well behaved" than functions in general. There are a lot of cases where they're simply easier to work with.
You can also think of it as "splitting" a function up into its linearly independent component functions (see https://en.m.wikipedia.org/wiki/Stone–Weierstrass_theorem ) which has further computational and theoretical applications

>>8453281
Linear algebra is extremely simple. It's the framework of 1/2 of shit. The problem is that teachers make it very very complex writing shit in retarded ways for no reason at all.

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>>8453619
Wew lad

Explain how I get value of K out of this?

For any geometry lovers I had this on a test today to which I left blank cause I had no idea:
Construct a trapezoid having given an angle, 2 diagonals, and the midline.

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>>8453624
whats the integral equal to once you actually input the bounds?...

>>8453615
Okay, autist. It still holds that you can take the derivative with only the power rule.

>>8453627
(0) - (k/2)

pls no angry

>>8453500
Bumping this in hopes of an answer.

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>>8453630
good job! now set that equal to 1

>>8453626
That makes no sense.

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>>8453638
K=-2

How can I be sure this is the correct answer, senpai?

>>8453642
Kek. Nvm I see the probabilty density is equal to 1

>>8442914
Why is the Ampere an SI unit instead of the Coulomb?

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>>8453629
>It still holds that you can take the derivative with only the power rule.
term by term differentiation requires uniform convergence

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>>8453626
>>8453639

>>8453657
My prof said he would take one from the book, I found it, obviously I never did it but what I said is literally what you're generally given in these questions, they can be easy or nightmares.

>>8453559
Have you been introduced to taylor series yet?

1) finite order taylor expansions are just approximations, depending on how accurate you want to be, you can get explicit bounds for the error depending on how many terms you use. If you want to be exact you need the taylor series, which is a convergent power series for analytic functions.

2) Again, it depends on how big or small you want your error to be

3) I'm not sure what you mean, but some functions such as polynomials are equal to their finite order taylor expansions (if the order is equal to the degree of the polynomial)

4) Taylor series/polynomials are magical because it allows you to rewrite functions as a polynomial, and polynomials are nice.

2)

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>>8450804
Let's find my wave physics textbook and give it a try.
For simplicity, I'll assume that the loudspeakers are point sources that emit circular waves in a plane. Pic related shows their arrangement.

For fun, a short description of what's going on:
The displacement (of air) caused by a sound wave can be described by a sine:
[math]D=A\sin(\boldsymbol{\phi}), \boldsymbol{\phi}=kr−\omega t+\phi_0,[/math] where
[math]A[/math] is the amplitude,
[math]k[/math] is the wave number [math]\frac{2\pi}{\lambda},[/math]
[math]r[/math] is the radius from the wave source to the observer,
[math]\omega[/math] is the angular frequency,
[math]t[/math] is the time, and
[math]\phi_0[/math] is the phase constant.
Each sound wave will cause a displacement (of air) at P. The total displacement is the sum of all the displacements according to the principle of superposition:
[math]D(r,t)_{tot}=D_1+D_2=A_1\sin(\boldsymbol{\phi}_1)+A_2\sin(\boldsymbol{\phi}_2)[/math]

Now, for the actual solution.
The two loudspeakers emit the same frequency and amplitude. The amplitude of the superposition of two such waves is given by
[math]A_{tot}=|2A\cos(\frac{\Delta\boldsymbol{\phi}}{2})|,[/math] with
[math]\Delta\phi=2\pi\frac{\Delta r}{\lambda}+\Delta\phi_0.[/math]
The amplitude is maximal (maximum constructive interference) when [math]\Delta\phi=2\pi n,n\in\mathbb{N}[/math]
The waves are in phase. Here, I think this means that [math]\Delta\phi_0=0,[/math] so we want
[eqn]2π\frac{\Delta r}{\lambda}=2\pi n \Leftrightarrow \frac{\Delta r}{(\frac{v}{f})}=n \Leftrightarrow f=n\frac{v}{\Delta r},[/eqn]
where [math]\Delta r=19−15=4, v=343[/math]m/s.
This is true when f is an integer multiple of 343/4 = 85.75
Therefore, the frequencies in the range [30,400] that maximize intensity at P are:
85.75, 171.5, 257.25 and 343 hz.

I think that should do it.

>>8453559
> Why we allow ourself to neglect higher order terms?
For |x|<1, |x^n|<|x|, i.e. the x^n gets smaller as n increases. Also, the factorial in the denominator grows quite rapidly, so unless the coefficients grow exponentially, the sum of the (infinitely-many) higher-order terms is finite and small compared to the sum of the leading terms, even for |x|>1.

> Exactly how do I chose what terms to neglect?
It depends upon how hard you want the problem to be. If you're doing this for some practical reason (rather than writing a textbook_, it depends upon a) how large a range of x you want to support, and b) how quickly the coefficients grow. Ideally, you'd prove an upper bound on the error for a given range of x and a given number of terms.

> is it not an approximation?
A Taylor polynomial (the series truncated to a finite number of terms) is an approximation. The infinite series is exactly equal to the function provided that the series converges (which, unless the coefficients grow exponentially, it will, as n! grows faster than x^n for any finite x).

> How should I recognize when solving a problem that Taylor expansion is a necessary or reasonable course of action?
Are there any alternatives to Taylor expansion? E.g. most functions don't have a closed-form integral, but any polynomial does.

>>8453648
Easier to define in terms of other base units. You can create a reference using a current balance, with a coil of given dimensions on one side and a given mass on the other.

With modern technology, there may be an advantage to defining the coulomb as a given number of unit charges. It's entirely possible that will happen at some point, in the same way that the metre and second were redefined.

>>8453694
>The infinite series is exactly equal to the function provided that the series converges

Not true, the function has to be analytic. There are examples of smooth functions that have convergent taylor series but are not equal to them. Of course most of the functions we care about are analytic so it's mostly ok

Complex analysis is nice because shit like this doesn't happen, smooth=analytic

>>8448237
Nice electrolysis you made there.
Google Faraday's Law and electrolysis.
Also, if you want to cover the plate completely, you'll need more current and more time (See Faraday's Law) and it happened because electrolysis. So go check it out. You are producing a reaction by adding electrons to the solution.

>>8450896
D U A L
N U M B E R S

>>8442914
could cannabis treat cabin fever in space?

>>8448237
Edges and pointy points have a larger charger density and a strong electric field. You need to wait more or give it more juice.

>>8453773
>smoking
>in a environment where oxygen and clean air is at a prime
Pothead logic everyone

I'm looking for a function, f(x), such that the limit of f(x) as x -> 0 is infinity but the limit of the derivative exists and is neither negative infinity not infinity.

I've tried the obvious solutions such as 1/x and -tan(x-pi/2) but I'm running out of ideas here. i can't make it work wit natural logs or e^-x. I feel like theres something fundemental and easy I'm missing

>>8453784
>implying burning pot is the only way to reap its benefits

I know it's not quite a /sci/ question but

what causes some ugly social dynamics like a shift towards elitism and subtle but effective mocking of high-performing students in smart collectives? What causes people to loose their kindness and understanding for each other?

Is it a sign of the synchronised burnout? Is it because dumb but social people establish this for the fear to loose their position? Is there a term for this process, studies, prevention?

>>8453707
Thanks.

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Hey guys how would i go about simplifying this?

wtf am I doing it wrong should it not be

(0.6)(350)/1????

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>>8454007

>>8454012
350*5/11 = 159.09(09)N

The hinges are +/-0.55m vertically from the centre of mass, and 0.50m horizontally.

The torque at the midpoint between the hinges is zero, thus 50*350=2*55*F => F=350*50/110.

>>8453802
I don't think it's possible. If you draw it, you'll see that in order for your curve to go to infinity in finite time, you'll need a derivative that grows arbitrarily large.
The argument is just the mean value theorem:
Assume [math]f'(x) \to l > 0[/math] as x goes to 0. Now there is an [math]\eta > 0[/math] such that you can write [math]\frac{l}{2} \le f'(x) \le \frac{3l}{2}[/math] for [math]|x| \le \eta[/math].
Now [math]|f(x) - f(\eta)| \le \frac{3\eta}{2}|x - \eta|[/math] for [math]|x| \le \eta[/math] so f is bounded around 0.

>>8450811
P=transition matrix
n-step transition matrix=P^n

all there is to it desu

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Hi /sci/ i know im pretty much retarded and should kill myself, but can one of you give me a way to solve this without using the cubic formula

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>>8454326
Pull your denominator over to the RHS, square both sides, expand it out and solve for alpha.

Or not.

I'm trying to get the wave function of a particle in a one-dimensional box with edges at -L/2 and L/2. The function should be a cosine function but what I'm getting is the following:

[eqn]\frac{\textrm{d}{\psi^2}}{\textrm{d}x^2} = -k^2\psi \to \psi = A\sin(kx)+B\cos(kx)[/eqn]
[eqn]\psi (-L/2) = 0 = A\sin(-kL/2)+B\cos(-kL/2) = -A\sin(kL/2)+B\cos(kL/2)[/eqn]
[eqn]\psi (L/2) = 0 = A\sin(kL/2)+B\cos(kL/2)[/eqn]
[eqn]\psi (-L/2) + \psi (L/2) = 0 = 2B\cos(kL/2) \to B = 0[/eqn] and
[eqn]\psi (-L/2) - \psi (L/2) = 0 = 2A\sin(kL/2) \to A = 0[/eqn]

What am I missing here?

>>8454375
Doesn't that require me to solve a cubic? After squaring both sides and expanding a bit it will look like:

2*a*(3-a) = 62.75^2*4*(1-a)^2*(1-a)

6*a-2*a^3 = 62.75^2*(1-a)^3

>>8454395
> Doesn't that require me to solve a cubic?
Yes.

The factors of 2/(3-a) in numerator and denominator cancel, leaving you with
a*sqrt(3-a)/sqrt((1-a)^3)=62.75
=> a^2*(3-a)/(1-a)^3=62.75^2
=> a^2*(3-a)-62.75^2*(1-a)^3=0
There's nothing about that form which makes it any easier to solve than any other cubic.

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How do I solve sup A and min A from this? I don't know even where to begin.

>>8454443
the set has no minimum
the sup is 11/2

>>8454443
Inf A*

>>8454446
the inf is 4

>>8454445
> the sup is 11/2
It would be if you replaced N by N*.

>>8454464
no, if the set contains a max then the max is the sup...

>>8454445
So, basically you can check sup and inf by using 1 and 0 respectively ? How abou

>>8454473
no, you check sup by finding the smallest number that is at least as big as anything in the set

and the inf by finding the biggest number that is at least as small as anything in the set

the number 4+3/(2n) gets smaller as n gets bigger so the max and sup is 4+3/2 and as n increases 4+3/(2n) gets arbitrarily close to 4 but is always greater, so 4 is the inf, no minimum

>>8454475
>no, you check sup by finding the smallest number that is at least as big as anything in the set

Then for 5+4/(3n) I would use 2 to find sup.
6+5/(4) I would use 3...
And so on?

>>8454483
no

please go read the definition of sup

>>8454485
OK. Thank you senpai

How could I interestingly represent data that looks like this:

Reached 1000 on 1st January
Reached 2000 on 3rd March
Reached 3000 on 28th March
...etc

The "obvious" thing is to plot date vs number but because the dates aren't linear the whole thing looks retarded. I have a few hundred samples in the set, but they are all formatted based on 'date reached'.

>>8451293
Are a, y, and z all independent variables or are they constants?

I have a system of stiff ODEs that I'm solving numerically in MATLAB, and my system is pretty poorly behaved in some parameter spaces in most solvers. Specifically, it keeps over-correcting and shooting down to negative values even though it's mass balanced and that shouldn't be possible.

Is it kosher if I put some manual clamping in my derivative function so that if that happens it just goes specifically to zero instead of shooting negative?

>>8452969
First, let x=c, where c is positive. Now that you know x is positive, you can remove the absolute values from the expression, and it is trivial.
Next, let x=d, where d is negative. Now you can remove the absolute values and replace the contained value with -d, and it is trivial again.
Since those two cases taken together, x being positive and x being negative, account for all possible scenarios when x is real, you have proved it.

>>8454307
I played around with a few functions and found sin(1/x)+(1/x). The derivative -(cos(1/x)+1)/x^2 seems to tend to 0 as x tends to 0 but I'm not 100% sure.

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Isn't the right way the most logical way to write integrals. This thing always bothered me

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>>8454949
Are you by chance afflicted by a surplus of mass?

>>8453598
You dont need to prove that the derivative of e^x is e^x. That is simply the definition of e.

Taylor expansions are very useful in other ways though. If you ever type a trigonometric or exponential function into a calculator, that's how it is able to give you a numerical answer.

>>8453598
>>8453620
>>8453680
>>8453694
Thank you very much! Much appreciated.

>>8454489
He used n=1 in the first problem because because thats the smallest possible n in the given domain

>>8454521
If the values 1000, 2000, etc are linear, you could flip the axes and have the dates be the y axis. Otherwise, I'm not really sure what you're trying to do because "interesting" is very subjective.

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What is the method to solve this?

>>8454932
The limit as x goes to 0 for that cos function doesn't exist. Regardless of x, cos will oscillate from -1 to 1, so the numerator will oscillate from 0 to 2 while the denominator shrinks rapidly. The result oscillates between zero and a huge negative number, so there is no defined limit.

>>8455260
the definition of a probability distribution is all you need

>>8455260
You just do a multivariable integral of that function over x and y and set it equal to 1 since pdf's always equal 1. The only variable left will be k, so you can solve for it. If you're unsure, just look up how to do a multivariable integral, and a piece-wise integral.

>>8454949
That's the way integrals are written, though..............

>>8455253
So with the natural numbers, when the domain is defined to be N, I should just roll with 1 to find it?

>>8455480
Not necessarily. That particular function is decreasing, so it's obvious that the sup occurs for the first possible value of n, n=1.

In general, the sup is essentially the same as the max, and inf is the min, except for one exception. If the function is bounded by a value that it never actually achieves, such as 4 in the example, then clearly there is no min, but 4 is still considered the inf.

>>8454949
I usually see them written the way on the right, but it doesnt really matter.

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>>8455300
>>8455295
>>8455260

I have integrated first with you with no luck. Then with x first then no luck... how to get K??

>>8455528
the output of an integral is a number, not a function you brainlet

>>8455528
Looks like you integrated by y, then started over and integrated by x. You need to integrate by y and then integrate the result by x.

Also, in this example, since the bounds of y are in terms of x, you must integrate by y before x.

>>8455585
What did I do wrong with integrating with respect to y. It seems to cancel out to 0

>>8455528
You need to integrate wrt y first, because the integration limits for y involve x.

But your integration is way off.

The indefinite integral of x*(x-y) wrt y is x^2*y-x*y^2/2+C. The integral over [-x,x] is 2*x^3.

The indefinite integral of that wrt x is x^4/2+C. The integral over [0,1] is 1/2.

=> k=2.

>>8455570
Depends if its definite or indefinite, brainlet.

>>8455591
Thank you. I see I missed intergral wrt y on x^2 completely.

Was this easy for you...?

I'm new to this and did not know the method to go about at all.

>inb4 brainlet

>>8455592
good thing its not when you're looking at probability distributions brainlet

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>>8455595
no bully pls

>>8455593
Polynomials are the one thing I can actually integrate without needing a computer to do it for me. Anything which requires recognising standard forms is out of the question (you forget that stuff if you don't use it regularly, and I've barely used it in the couple of decades since school).