New SQT

take a picture and give it to whoever asked u

>>8454762
A book doesn't really help.

Set up the equation of an arbitrary line which belongs to the plane, take the dot product with the original line, show it equals zero.

Alternatively, find the equations of 2 perpendicular lines which belong to the plane, take their cross product, show it is co-linear to your original line

>>8454774
No hablo espanol

>>8454755
Remember that the vector <1, -2, 3> is normal (perpendicular) to that plane.

>>8454784
Isn't every perpendicular line the normal?

>>8454755
the equation of a plane x-2y+3z=9 can be written as [math] \begin{bmatrix} 1 & -2 &3\end{bmatrix} \begin{bmatrix} x\\y\\z\end{bmatrix} = -9[/math]

So you are taking the dot product with the normal vector, and this is parallel to the vector defining your line [math] \lambda(-1,2,-3) [/math]

>>8454796
Yeah but it won't workerino

>>8454819
op is a faggerino

>>8454822
Helperino porfavorino

If I run full wave rectified electricity from a 50Hz AC source through a heating coil, is it worse than balancing it with a capacitor? Like will there be any downsides not using a capacitor, in terms of the heating element breaking down faster, or temperature not being as stable, or anything else?

>>8454755

saged

>>8455098
Pls no, help me
>>8455093

Which one is better for newbie?
this https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877/ref=pd_sim_14_5?_encoding=UTF8&pd_rd_i=0387967877&pd_rd_r=CH4SZWSW2ZVTCC5CVM10&pd_rd_w=c6Oye&pd_rd_wg=ceM9e&psc=1&refRID=CH4SZWSW2ZVTCC5CVM10
or this
https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773/ref=mt_paperback?_encoding=UTF8&me=

>>8455125
Gelfand.

>>8455141
Why? Seems like serge lang very popular among imageboards.

>>8455219
lang is popular among neckbeards

gelfand is what you want

you realize both are readily available to download right? you don't need to ask for an opinion online and ask for reasons for that person's opinion, just open the book

I'm quite interested in neural networks and AI, but i only have very basic programming skills.

What literature or reading list could /sci recommend to prepare me for/introduce me to these topics?

>>8454827
How do you want us to answer this? What exactly are you looking for?

>>8455488
There's a (free) coursera course in Machine Learning that opened on the 31st. It's good for an introduction.
https://www.coursera.org/learn/machine-learning

well the normal vector to the plane is <1,-2 3>

The line points in the direction <-1,2,-3>

Since the direction vector of the line is a multiple (c=-1), r is perpendicular to the plane.

>>8454755
The plane x - 2y + 3z = -9 is parallel to the plane x - 2y +3z = 0, so a line is perpendicular to one must per perpendicular to the other (and vice versa). The vectors included in the plane x - 2y + 3z = 0 are all of the vectors orthogonal to (1, -2, 3), so (1, -2, 3)*t, where t is a real number, is the line perpendicular to the plane (that happens to pass through 0). In general, you can add a vector to a line, and that new line will be parallel to the original, so (6, -5, 1) + (1,-2,3)*t would be perpendicular to the plane. Taking lambda = -t, we get (6, -5, 1) + lambda*(-1,2,-3) is parallel to lambda*(-1,2,-3), which is perpendicular to the plane x - 2y + 3z = 0, which is parallel to x - 2y + 3z = -9, so (6, -5, 1) + lambda*(-1,2,-3) is perpendicular to x - 2y + 3z = -9.

How does using Lagrange interpolation to find the derivative of a set of points work?

Let's say that I have (x1,y1) (x2,y2) (x3,y3), I know how to use the polynomial to get a function, let's say P(x) = 15(xxx+12xx-15). Then I just have to derivate that function? Am I on the right track or is it a different procedure when you're asked to get the derivative?

How do I understand action?

>>8455093
To a heater, there's no difference between rectified AC and non-rectified AC. But adding a capacitor will increase the power (both drawn and dissipated) by up to a factor of 2, as you'll be applying the peak voltage rather than the RMS voltage.

>>8455620
A set of points doesn't have a derivative.

However, if you assume that those points are samples of some unknown function, then in the absence of any other information, the Lagrange polynomial is a reasonable guess as to the function. And you can find the derivative of a polynomial.

tl;dr: yes; find the Lagrange polynomial and differentiate it.

Say that, using Lagrange multipliers, I was able to find some points that may be maxima/minima of a function under certain constraints. How can I actually proof that they are actually max/min? Do Hessian matrices still work under constraints?

Anyone else feels insecure about asians and their science skills/self-discipline?

>>8455723
Ask Feynman:
http://www.feynmanlectures.caltech.edu/II_19.html

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Help me make sense of this. It says [math]f[/math] is convex. And it also says that [math]g[/math] is equal to [math]f[/math]. What's there to prove about [math]g[/math] being convex?

>>8456454
write down what it means for f and g to be convex and you'll see what you need to prove

>>8454755
if you don't know why this is true you need to drop the class and stab yourself NOW

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Can't figure out which portion of text in b) I should refer to

>>8456675
And I have no idea how to solve c) as well

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>>8456681
Duck me

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Can this be colored with three colors?

I'm pretty sure it is impossible, but how do I go about proving this? It is possible with four colors.

>>8456869
>It is possible with four colors.
Are you sure? Look at the right side of your pic, that piece is in contact with 4 other pieces, so no matter what color it is it will be touching another piece of the same color. Unless I'm completely misinterpreting what you're asking.

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>>8456910

>>8456910
There was a thread on this last night
>Four Color Theorem

>>8456869
Just go about adding vertices and edges but change the lower bound in a similar fashion for four color and see what you get. If your lower bound > sum then it's not possible.

>>8456927
I feel pretty dumb now

>>8456869
It cannot be colored in three colors. Start from the outside in. The coloring is forced, and it gets stuck.

>>8454755
The first thing is growing with respect to the vector (-1,2,-3) but the second thing is a dot product with respect to that same vector equal to a constant. So the projection of an arbitrary value onto that vector never changes which means it must be perpendicular.

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>>8456869
You can get pretty close by using only 3 colors.

>>8456930
Not sure what you mean to calculate the lower bound? I see that there are 20 vertices, but I'm not sure how to show it is impossible.

>>8456980
>>8456980
Like I get from this and my own drawing that there will be two spots that are forced to be a fourth color, but how do you show that there isn't a more optimal coloring?

>>8457104
>but how do you show that there isn't a more optimal coloring?
Well in this case there's only 3 colors, so the only other way to color this thing is if you swap two of the colors, in which case it will be the same result.

How do you find the Hessian of a quadratic function [math]f(x) = \frac{1}{2}x^TAx + b^Tx + c [/math] for a symmetric matrix A?

I know it should be equal with A, but I don't really understand how to get there..

Is Computer Science truly a meme?

>>8457142
Set the equation equal to 0

>>8457151
And?

>>8454755
statsfags:

do the inputs to a gaussian process emulator need to be strictly gaussian?

I know some engineering maths... no pure maths or anything. And I know linear algebra with eigendecompositions, jacobians, this kind of stuff. But where do people pull terms like homeomorphic, ring, topology, etc? People seem to define linear algebra concepts using this stuff sometimes, but no one presented this to me in any of my courses

>>8457226
That's because they're pure maths terms. I'm guessing you've taken a basic linear algebra course designed for engineers. If you want to dig in and learn the lingo, pick up a more rigorous, proof-based linear algebra text like Hoffman-Kunze. And take a look at abstract algebra, too.

Consider a set of functions which go to zero (as x tends towards infinity or negative infinity) faster than [math] \frac{1}{x} [\math]. Is there any way to show that the derivatives of any function in this set are also elements of this set? (Or is it even true?)

I'm currently thinking of using a series expansion in terms of Hermite Polynomials to show this but I feel like it's not watertight.

>>8457260
Ehhh I have enough on my plate right now. I guess I'll just continue to ignore them

>>8454755
Two vectors are perpendicular if and only if their dot product is zero.

The normal of your plane is (1,-2,3) and the name is suggestive: that vector is perpendicular (or normal) to every vector in the plane.

You have the slope of the line and the slope of the normal of the plane. Can you think of a way of using these two facts to show what you're asked?

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is there some canonical way to recombine the linearizations of a nonlinear system about its various critical points into an estimate of the original system

>>8456869
For maps where all nodes have 3 arcs (such as the map you posted), if any region has an odd number of adjacent regions, the map cannot be colored with 3 colors.

I used to work on the four-color problem with my uncle and the above was one of my discoveries at a young age. I'm sure it somebody else discovered it long ago, though.

It has to do with the ability to alternate 2 colors around a region. The proof should be easy.

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How do people do this shit? How to transform a quadratic function to symmetric form? People just started doing I'm not following the last step here. Is there some formula?

>>8457555
I should add that for those types of maps, if all regions have an even number of adjacencies, then the map can always be colored with 3 colors.

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How the fuck do I even go about solving this:
INB4 Brainlet math, I'm reviewing Trig

Differential Equations question:

For Cauchy-Euler type DE, what do I do if my Auxiliary Equation is:

(m^2 + 1)^2 = 0

?

>>8457591
>sen

>tg

What in the actual fuck?

Is there a trick to tell right away that the matrix below is not positive semi-definite?

[math]\begin{bmatrix}4 & 4 \\ 4 & -2\end{bmatrix}[/math]

>>8457599
It's my language:
Here it's Seno (Sine) and Tangente (tangent).
That's why it looks weird as fuck

>>8457591
what's hard to get here?
write a general quadratic from with a symmetric matrix, decompose it and that's it. your formula.

How r u this dumb Mr. high school?

The direction vector of the line (the term with the parameter Lambda in front) is a scalar multiple of the plane's normal ((A, B, C) is the normal of a plane with the Cartesian equation Ax + By + Cz + D = 0), meaning they are parallel.

Since the line is parallel to the plane's normal, it must be perpendicular to the plane, since the normal is defined as being perpendicular.

Got it kid?

>>8457603
negro de mierda
use the sen(a+b) =sen a cos b+ sen b cos a
formula. and other similar formulas

>>8457591
There's nothing to solve, these are just plain expressions

Why do schools waste time on this crap, why can't we overhaul the mathematics education system from scratch to use CASs for this kind of trivial bullshit

>>8457618
can be simplified tho.
lots of unnecessary pi terms

So i have been downloading like 3gigs of porn everyday for some weeks. The problem is I cant watch full length videos and keep pressing the Right key to go through the whole video in under a minute. Whats wront with me and how do I fix that?

>>8457666
Stop watching porn. It's bad for you mental health.

>>8457671
How?

>>8457673
Cancel your home internet. If you can watch porn on your cell phone, get rid of it.

You have to starve your addictions. Right now your brain is addicted to self-destruction. When you start doing healthy things, your brain will try to do everything it can to stop you. It will throw the kitchen sink at you. Push through it. Once you get over the hump, your brain will start to be reprogrammed to feel good when you do healthy things.

>>8457666
Find the type of porn you like and stick with that. The majority of pron is garbage. Either they have a long drawn out setup, or the virgin cameraman is saying dumb ass shit the whole time, or the routine is generic, etc. Once you find a quality video, just sit there and be patient without touching your dick for while. Let yourself get into the mood naturally, and only start jacking off when it's impossible to resist.

>>8457671
>>8457697
This is retarded. Porn """""""""""""""addiction"""""""""""""""""""""' is such a meme.

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How do I find the miller indices of a crystal face given only a photo? I could figure it out if I had a protractor or a ruler, but I don't have the time or the resources to do so on the exam.

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>>8457104
> how do you show that there isn't a more optimal coloring?
By contradiction.

Assume that it's 3-colourable. Start at the red area in pic related. The two areas to its right must differ from the red area and from each other. So now you have 3 areas with 3 distinct colours.

Any area touching both red and green must be yellow, any area touching both red and yellow must be green. That dictates the colours for the other four areas touching the red area.

Clearly, any 3-colouring of those 3 cells is equivalent up to permutation of the colours. The areas around the edge must all differ from the centre, so they can only use 2 colours, which must alternate.

The pink area on the left touches both green and yellow, so must be red. The cyan area touches both green and yellow so must be red. But the cyan and pink areas touch each other, so cannot both be red.

Ergo, the graph isn't 3-colourable.

>>8457226
Engineering tends to equate linear algebra with linear algebra over the complex numbers (or even over the reals). But it can be applied to anything which has addition and multiplication.

>>8456869
Yes. It's a triangle-free planar graph so it is 3-colorable.
It's not 2-colorable because it has odd cycles.

>>8456927
Dude what the fuck is up with the penmanship of people today? I cannot believe that adults today have handwriting like fucking first graders when I was a kid.

>>8457560
If you expand out x^T.M.x, you get a sum of terms of the form
x[i]*M[i,j]*x[j] = M[i,j]*x[i]*x[j]
for all i,j.

But x[i]*x[j]=x[j]*x[i], so you can combine pairs of terms
M[i,j]*x[i]*x[j] + M[j,i]*x[j]*x[i] = (M[i,j]+M[j,i])*x[i]*x[j]
then split them in half:
(M[i,j]+M[j,i])*x[i]*x[j] = (M[i,j]+M[j,i])/2*x[i]*x[j] + (M[i,j]+M[j,i])/2*x[j]*x[i]

So you end up with a symmetric matrix M' where
M'[i,j] = M'[j,i] = (M[i,j]+M[j,i])/2

and x^T.M.x = x^T.M'.x

>>8457759
> Dude what the fuck is up with the penmanship of people today
What is this "pen" of which you speak?

The only time I use a pen is if I need to make a note and I'm not near a computer. Otherwise, I type.

>>8457759
Because the little faggots didn't go to a school that properly taught them discipline, and thus spent all their schooling years picking their nose instead of learning how to write correctly.

>>8457759
go to bed gramps

How do you guys do this? I mean I saw a lot of you guys learn math/chemistry/physics/comp.sci at the same time. How do you have so much time to learn all this stuff? And why don't you learn one particular area (for example only math) instead of learning others subjects like chemistry?

>>8457798
t. brainlet

>>8457591
Symmetries.
sin(-x)=-sin(x)
cos(-x)=cos(x)
sin(π/2+x)=cos(x)
cos(π/2+x)=-sin(x)
tan(x)=sin(x)/cos(x)

IOW, all trig functions can be expressed in terms of one quadrant of sin(x).

>>8457832
>calling someone a brainlet in a stupid questions thread

Who's really the dumb one in this situation?

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Can anybody explain me this one? (universe of discourse is the Natural numbers)

I am trying to go through How to Prove it and had some trouble with pic related.

I'd say the statement (x < 10) ----> (y < x ----> y < 9) is true.

But what makes me question my answer is the universal quantifies. Making me think that it is not true for all values of X and all values of Y.

>>8457920
it is the same
have you tried assuming it is false, and showing a contradiction

>>8457920
> I'd say the statement (x < 10) ----> (y < x ----> y < 9) is true.
For which values of x and y would you say that it's true?

If you'd say that it's true for all x and y, then you'd put universal quantifiers in front of it. And you can move the quantifiers around so long as it doesn't affect which variables they capture (so moving the forall-y inward past the (x<10)-> changes nothing.

An expression with free variables is a predicate, which may be true for some values of those variables and false for others. Whereas an expression with no free variables (i.e. where all variables are bound by a quantifier) is either true or false.

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>>8457267
Please Help ;_;

https://en.wikipedia.org/wiki/Medea_hypothesis
I thought multicellular life originated 1500 Mya. Why would the Medea hypothesis care about mass extinction events which occurred before then?

Is there an algebraic expression for a curve formed the positive part of -x^2 +1 and x^2 -1

>>8458225
y=|x^2-1|?

Or did you mean something else?

>>8457267
By goes to zero faster than 1/x I assume you mean [math] \lim_{x\to\infty}xf(x)=0[/math].

let f(x)=sin(x^3)/x^2. It's clear that the limit of xf(x) is zero as x goes to infinity/negative infinity.

But f'(x)=3cos(x^3)-2sin(x^3)/x^3, which doesn't even go to zero as [math] x\to\pm\infty[/math]

>>8458374
Much appreciated senpai.

>>8454774
Actually, you just have to take the cross product of two non-parallel lines in the plane and show that it's parallel to the line in question.

>>8458389
Actually you just have to show that the line is parallel to the normal vector of the plane.

Determine whether the sequence {a_n} where a_n = 2^n for every nonnegative integer n, is a solution of the recurrence relation given a_n = 5

I want to know if this is a proper solution

a_n = 2^n
a_n = 5
5 = 2^n
n = ln5/ln2

since n is not an integer, it follows that a_n is not a solution of the recurrence relation.

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I'm having a tough time visualizing this problem. Are there any programs where I can rotate shapes and think about a problem like this? I don't have any cubes here to help me see it either.

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Is this right?

This is how we were taught to go about this problem. But the area below the x-axis should be considered separate as the area is negative and then add onto the area in the first quadrant.

How does it make sense to compute the entire area in one intergral. Also why isn't the area before x=-1/2 considered.

Help a brainlet out pls

>>8458925
Seems correct. The area before -1/2 isn't considered because you are not interested in it, as you want to figure the area of the enclosed curve. You just integrate the area above the x axis of the parabola between the two intersecting points and add that to the opposite of the area of the line, so they will be added in the third quadrant and subtracted in the first one.

Is there an intuitive explanation for torque beyond force*moment arm? I mean I know what happens in the real world, but like why is it like it is?

If you have a function in completed square form [math]f(x) = (x-c)^TB(x-c)[/math], Are there any linear algebra-y ways to find the minimum? i.e. using eigenvalues of [math]B[/math] or something? What theorem is this

In an intro QM class, how does knowing an operator is hermitian help me?

I've yet to fully apply its significance. I understand it's significant, but when I solve problems I'm not yet utilizing all of it's properties to help me.

>>8459296
>In an intro QM class, how does knowing an operator is hermitian help me?

Hermitian operators have real eigenvalues. Eigenvalues are the actual numbers you measure in an experiment, so it wouldn't make any sense for an observable to have complex eigenvalues.

>>8459307

I understand that.

But for example in chapter 3 of griffiths intro to QM book, there are cases where working through a problem you would make the statement

>well this operator is hermitian therefor i can just say this, thus reducing my expression to this which makes this whole process a lot easier

I've yet to confidently locate when that happens because I don't fully know what it's significance has on the outcome for most cases other than it provides a real observable, the eigenvalue.

I think I just need to practice more really lol

>>8459325
If you want to understand QM than read a Functional Analysis book instead of a QM book.

>>8459333

what book do you suggest?

>>8458325
I meant the postive part of -x^2+1 and the NEGATIVE part of x^2-1. Basically a closed cuve formed by a part of of a parabola and it's reflection.

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Why doesn't adding up the moments of the components working?

>>8459408
*work :^)

>>8459408
Can you post the question

>>8459416
Determine the moment of the 5kN force about point B

>>8459422
You fucked up with the signs calculatibg the moment of each component. Consider that when calculating, let say, the x component, you just need to change the y comppnent to 0 in the determinant. Then the samd shit with the y component and theb add them so you are basically doing the same in more steps.

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Hey guys, here's me hoping you can give me some guidance. First of all excuse me if I don't use the correct English terms for this question.

Basically I need to find the value of the inductance L1 so the phase shift between the voltage source and AB is 3.436 ms.

Now I can do this in Simulink and try random values until I get it right but I would like to know how to do it with a phasor diagram and trigonometry.

>>8456869
>Can this be colored with three colors?
Yeah, in fact it's already colored with one color, white.

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can you help me?

>>8459533
Use comas to separate coordinates you fucking retardes faggot.

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>>8459533

>>8459540
ok, thanks. Now the more important part.

p is given and u as well. How would I calculate q?

>>8459551
But do you understand what I did in >>8459540?

>>8459553
yes, you used Pythagorean Theorem.
I have not used maths in a long time. I migth be incorrect

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>>8459557
Ok anon here you go. This time instead of using u=6.71... I use its exact form.

>>8459540
This is incorrect.

>>8459627
It's right, but I never would have thought about solving the problem in that way. I did sqrt(36+9) and got the same answer.

How do i get gud at analysis? Seriously there is so much to remember to solve a lot of these problems / proofs. Am I wrong in saying that, calculus is the weed out course for people who don't have their elementary algebra skills down, and analysis is that for those who don't have all of the actual concepts and intuitions?

i fucked up my linear algebra classes (passed them but without knowing the whole subject due to how the evaluation was distributed). i'm thinking about reading Shilov's linear algebra or lax's linear algebra with applications. it is said that the last one is harder, but given that i've had an interaction with (most) of the (introductory) material, should i read it?
thank

>>8459795
check out 3blue1brown's videos to get an intuition of what is going on geometrically. After that, assuming you are comfortable with the basic computations (if you passed the class you should be) you should be safe to revisit the subject with the text your liking.

>>8459850
thanks a lot, my doubts came almost exclusively from the geometrical interpretations of matrices, hope it does help

How do I make a program on Matlab that asks the user to input a function? More specifically and R^n->R function.

>do homework
>learn concept and can do it
>take test over concepts in a chapter
>can't remember anything except the last thing I did
>do bad


how do i stop this

>>8459952
Review the concepts in the chapter before the test. This takes nothing more than to read over your notes and remind yourself of those concepts. If you need to, go over some of the homework problems again. Things don't just get stuck in your memory the first time you do them.

>>8457602
[0 1] A [0 1]' = -2

>>8459161
take the derivative and set it equal to zero Solve the resulting linear system

>>8459963
I try sometimes but it's like I completely forget how to do the problem.

I have to go through and reteach myself to do the problem which is easier than learning to do it for the first time but it still takes time.

>>8459985
This shouldn't concern you. Studying and learning takes time and effort. There's no magic pill that causes you to remember everything you've learned. So first, come to terms with the fact that you will have to invest time if you want good grades on the exams. Then, do a decent amount of exercises. If you do a certain type of problem several times, it will get ingrained in your head. You will probably forget some of the details the day before the exam, but if you're a normal person and don't have some sort of severe memory issue (you probably don't), you will probably be able to remember the gist of the solution, and you can recall the details by reviewing.

>>8460029
I think it wouldn't be as hard if I enjoyed math and did it more.

>>8459523
At 50 Hz, 3.436 ms = 2*pi*3.436/20 = 1.07945 radians. The tangent of this angle is 1.86875.

The voltage across AB is 213*I. The voltage across the inductor is j*2*pi*50*L*I. The input voltage is the sum of those two, (213+j*100*pi*L)*I.

The output voltage is in phase with the current, so the phase shift between input voltage and output voltage is the same as the phase shift between input voltage and current, i.e. the argument (angle) of 213+j*100*pi*L, which is arctan(100*pi*L/213).

So 100*pi*L/213=1.86875 => L=1.267 H.

Working backward (calculating the phase shift of the input relative to the output) is arguably simpler than forward because it keeps j in the numerator.

But note that arg(1/z)=-arg(z):
arg(a*b)=arg(a)+arg(b)
arg(1)=0.
0=arg(1)=arg(z*(1/z))=arg(z)+arg(1/z)

>>8459905
Let us know if it helps. Of course it is a rather soft and supplemental way to learn the material. Definitely do some practice problems in R^2 and R^3 to further master the basic intuitions.

>>8460160
Thank you Anon, I'm going to work on that right now.

>>8460211
it is, but i hope going through the book will make it not as soft, as i'd like to learn the material in-depth.

>>8456910
The fact that you can do it with 4 colours is actually a proven result from graph theory.

>>8460299
>proven
i guess if you subscribe to the notion computers can do mathematical proofs...

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>>8456869
>Can this be colored with three colors?
That was easy

>>8460310
Your mom was easy last night

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>>8460310

>>8460302
Why couldn't they? The validity of a proof doesn't depend upon whether it was created by a human, a monkey, a computer, or a random number generator which just happened to spit out a valid proof.

Interestingly, the four-colour theorem was one of the first to be proven with the aid of a computer (although not entirely /by/ computer).

very simple maths question lads
i've been asked to solve sinh(x) = a specific value
the furthest i've got in finding it is
e^x - e^-x = a value
how do i proceed from here? or have i gone down the wrong route already?

>>8460375
Just use the inverse hyperbolic sine function?

>>8460380
i feel like that can't be the answer they want as it's a five mark question. It also asks to explain why there is only 1 solution to this question

Simple physics question

In elastic collisions, kinetic energy is maintained. But is that kinetic energy in each individual object or just total system kinetic energy?

>>8460383
Total

>>8460383
total system

>>8460382
If it gets you the right answer and it's mathematically sound, then what's wrong?
Also, sinh is one-to-one, so obviously there is only one solution.

>>8460385
>>8460386
thanks

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>>8458184
Shilling my question one more time.

>>8460375
Put x=log(q) => e^x=q => e^-x=1/q
e^x-e^-x=k
=> q-1/q=k
=> q^2-k*q-1=0
=> q=(k±sqrt(k^2+4))/2
=> x=log((k±sqrt(k^2+4))/2)
However ...

>>8460382
for all k, k^2+4>k^2
=> sqrt(k^2+4)>sqrt(k^2)
=> sqrt(k^2+4)>k
=> k-sqrt(k^2+4)<0
Thus, log((k-sqrt(k^2+4))/2) isn't real, so the only real solution is
x=log((k+sqrt(k^2+4))/2)

>>8460389
> If it gets you the right answer and it's mathematically sound, then what's wrong?
What's wrong is that the question is essentially asking for the definition of asinh() in terms of more fundamental operations.

"Solve e^x-e^-x=k for x" amounts to "Solve 2*sinh(x)=k for x". And I don't think "x=asinh(k/2)" would be accepted.

>>8460160
Jesus Christ man it was so easy after all!
I used sin and cos instead of tangent but you helped me get the intuition for this.

For some reason circuits are very hard for me to understand, even though vectors and trig didn't give me so many problems.

Thank you!

How do I get better at recognizing how to factor stuff like this? I know I need to practice more, but from where exactly?

Also how did they factor this?

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>>8460475

>>8460411
ln(k+sqrt(k^2+1)) is the same, but a bit more tidy

can anyone give me a list of all standard integration tactics, tips and tricks?

>>8460523
Refer to any decent calculus textbook. We're not going to list all that shit out for you nigga

how do i show the decideability of these two languages
l1 = { <M,w,n> | M halts on input w in <= n steps}
and l2 = same except >=n steps
is it correct/enough to say that l1 requires a finite number of steps so will eventually halt?
isn't l2 undecideable since it is able identify all languages that do not halt?
the answers just seemed to obvious so i feel like i'm missing something.

How do I show if J = [0,-1; 1,0] and O is an orthogonal matrix, then JO = detO * OJ?

>>8460545
what kind of calculus book goes autistic on this tho? i know how to integrate, I just want to know them tricks

>>8460609
Nevermind I got it.

>>8460495
Not quite. The original question (in >>8460375) was (effectively) 2*sinh(x)=k, not sinh(x)=k.

The expression in >>8460411 can be re-written as:
log(((k/2)+sqrt((k/2)^2+1))).

>>8460613
I don't know what you mean by "tricks," so this might not be what you're looking for. "Problems in Mathematical Analysis" by Demidovich has a chapter of integration problems, split into the following sections:

1. Direct integration
2. Integration by substitution
3. Integration by parts
4. Standard integrals containing a quadratic trinomial
5. Integration of rational functions
6. Integrating certain irrational functions
7. Integrating trigonometric functions
8. Integration of hyperbolic functions
9. Using trigonometic and hyperbolic substitutions for finding integrals of the form [math]\int R(x, \sqrt{ax^2 + bx + c})\, dx[/math] where R is a rational function
10. Integration of various transcendental functions
11. Using reduction formulas
12. Miscellaneous examples on integration

Each section has a short explanation of the method followed by a shit-ton of exercises. If you did all of those exercises you would be well on your way to being an integration mastermind.

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>>8460646
thanks a lot. yeah that's what I was talking about. integration techniques.
it feels as if i had forgotten how to do most non trivial integrals

>>8460523
1) can you immediately use a formula?
2)can you algebraically manipulate the integrand so as to apply formula(s)
3)can you use u substitution? That is, do you see a function and it's derivative in the integrand?
4)can you use integration by parts? That is, does the integrand consist of the product of two functions f(x)*g'(x)? Tip: you will be looking for two functions: one function such that when you differentiate it the integral becomes easier, and the other such that taking the anti derivative doesn't affect it much
5)am I integrating crazy looking trig functions? If so, can I simply them using the various trig identities I know?
6)is there a root with the sum/difference of squares in the argument? Use trig substitution.
7)if none of that applied you may have to use partial fractions

>>8457336
no

>>8457336
yes

>>8460684
>>8460706
Ok fuck you guys I'm going to /g/

>>8457336
>>8460706
>>8460684

maybe....I don't knoooowwww......can you rePEAT the QUEStion....*sick heavy metal guitarary*.....YOU'RE NOT THE BOSS OF ME NOW YOU'RE NOT THE BOSS OF ME NOW YOU'RE NOT THE BOSS OF MEEE NOOOOOW AND YOU'RE NOOOOOOT SOOOO BIIIIIIIG...*duh duh duh* life is unfair...

hahahahaha epin :XDDd

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I'm doing Oscilators in dynamics right now and I have no idea how they did this derivation. Where does this first identity come from?

>>8460818
Angle-sum identities:
cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)
sin(a+b)=cos(a)*sin(b)+sin(a)*cos(b)

These can be derived using rotation matrices. A rotation of angle a can be expressed as the matrix
[ cos(a) sin(a)]
[-sin(a) cos(a)]

Clearly, rotating by an angle of a+b is equivalent to the composition of rotations by angles a and b:
[ cos(a+b) sin(a+b)] = [ cos(a) sin(a)][ cos(b) sin(b)]
[-sin(a+b) cos(a+b)] [-sin(a) cos(a)][-sin(b) cos(b)]
=
[ cos(a)*cos(b)-sin(a)*sin(b) cos(a)*sin(b)+sin(a)*cos(b)]
[-sin(a)*cos(b)-cos(a)*sin(b) -sin(a)*sin(b)+cos(a)*cos(b)]

>>8460722
Said no one ever.

I don't get this shit. I know that for low temperatures, the magnetization of a paramagnetic material is of the form:

M = No*u.

But generally M = X* H.

How can I find the susceptiblity X for a paramagnetic material at 0 K ?

Hey guys I'm brushing up on my trig, in prep for the next part of my calc class and I can't for the life of me figure out how to prove this. I feel like I must be fucking retarded.

[math]
\frac{1 - sin2x}{cos 2x} = \frac{1-tanx}{1+tanx}
[/math]

I've gotten as far as

[math]
\frac{1-2cosxsinx}{cos^2x - sin^2x} = \frac{cosx - sinx}{cosx + sinx}
[/math]

but I don't really know how to proceed from here.

>>8460932
Nevermind, I am just fucking retarded. Spent ages on this and then as soon as I posted I realized what I had to do.

>>8456869
Dude I could color that with one color.

PS: When I was younger (probably 5 or 6), I had some guy come test me to see if I was a smarty pants. One of the tasks was to color a bunch of characters and I was nervous he'd mark me down if I went over the lines, so given that my only criteria was to color them I colored them all white.

Another question was "What's the capital of Arizona? And I replied with a confident "A".


Needless to say I've been confirmed retarded.

>>8460932
Why are you manipulating two sides of the equation though anon? In a proof only one side should be manipulated.

given this sum:
[eqn] \sum_{k=-1}^{n} 1/k! [/eqn]
what is done with the term where [math]{k} = -1[/math] ?
do you just throw it out, since -1! is undefined? is it zero? I'm not sure. please help

>>8461010
The whole sum is undefined if one of the terms is, which is this case since (-1)! doesn't mean anything

I would imagine in most individual cases where you could get this sum you can probably come up with a reason to throw it out though

>>8461010
The sum is undefined.

>>8460932
funny how that identity holds even if you swap all signs

>>8456685
>>8456675
underage

Materials science project. I need to select a material to use for a drill rod.

What material property best describes efficient transfer of force through the rod?

I feel like modulus and damping are related but not quite the right properties.

Hey guys, how would I go about finding the inverse of this function: f(x)=arctan(ln3x)

thx

>>8461970
nvm did it

>>8457602
https://en.wikipedia.org/wiki/Sylvester%27s_criterion

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What does the ||x|| = 1 here mean? What surface does it define?

Not sure we've covered this in lectures, but I need to know it for a question that's due in next week.

>>8462007
norm 1

looks like a integral over the surface area of a sphere but i could be wrong

>>8462007
For what course is this problem, anon?

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>>8462011
Looks like it could be with the 4pi/3 bit.

>>8462065
The module is called Vector Analysis, although really it's a mixture of that and complex from what we were told in the first lecture. Pic related is an outline of the course, which may be better than me trying to explain it.

How can I prove than an element m cannot be in both the sets [(2^k)n | n is a natural number and odd} and [(2^l)p | p is a natural number and odd} where k does not equal l and n does not equal p?

Could someone check my proof?

Theorem: if a function f satisfies f''(x) > 0 for all x in (a,b), then f must be concave up on (a,b).

Proof: Let f be a function such that f''(x) > 0 for all x in (a, b). Recall f is concave up on (a, b) iff f is differentiable on (a, b) and f' is strictly increasing (a, b).

Since f'' exists for all x in (a, b), f' exists for all x in (a, b) and thus f is differentiable on (a, b).

From a previous theorem we know that for a differentiable function, call it g, g'(x) >= 0 on I iff g is increasing on I. Now consider the function f'. Obviously d/dx[f'(x)] = f''(x). Since for all x in (a, b), f''(x) > 0, we know by the previous theorem f' is increasing on (a, b).

Can i f' is strictly increasing since we have f''(x) > 0 (strictly greater than)?

>>8462089
can you use the fundamental theorem of arithmetic (uniqueness of prime factorization)? if you suppose m=n(2^k)=p(2^l) then since n and p are odd they contain no factors of 2 so l=k, and so n=p

without that machinery you could consider n(2^k)-p(2^l)=0 which gives (2^k)(n-p2^(l-k))=0, which forces n=p2^(l-k). since n is odd you must have l=k and so n=p

>>8462096
Prime factorization is fine, thanks anon.

>>8462094
That last sentence should read

**can I say f' is strictly increasing on (a, b) since we have f''(x) > 0 on the interval

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I'm not sure how to prove any of these beyond a).

Its been bothering me the whole weekend.

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What's stopping me from not making x=x0. Why does it get only close to but I can't equal to x0

>>8462198
You can see in the definition of the limit that for all x, it must be the case that [math]0 < |x - x_0| < \delta[/math]. But if [math]x = x_0[/math], then [math]|x - x_0| = 0[/math], which is obviously not greater than 0.

It happens to be the case that sometimes the limit of a function as x approaches x0 is the same as f(x0), which is why you can just plug in x0 to find limits like that. But this isn't always the case. The limit is distinct from the function's actual value at that point.

>>8462198
Because the whole point of limits at a point is to see what value a function "should" take there. It might not actually be defined or it could equal something completely different than what you'd expect.

>>8462136

(d) is an open ellipsoid, so that is bounded. Complete the square to show it?

(c) Fix an x, and think of this as an equation in y. It is a cubic in y, thus always solvable, because every cubic has a real root. Since x can be arbitrarily large, this set is unbounded.

>>8462136
For (b), let X = x^2, Y=y^2, and get the equation of an ellipse in X and Y. Thus X and Y are bounded, and so x and y are bounded. Algebra get you an explicit bound, though there isn't much point.

>>8462007
Since it's two integrals and dA, it seems this is an integral over the standard sphere x^2+y^2+z^2=1.
{ x \in R^2 | ||x||=1} is the 2-sphere in R^3.

In that case, x is also the outward unit normal on this surface, so it's inner product with the gradient of f is the normal component of that gradient.

Is the tilde approximation of log(N^2 + 1)/log(N)

~2log(N)
or
~2

>>8462302
2
log(N^2+1)~=log(N^2)=2*log(N)
log(N^2+1)/log(N)~=log(N^2)/log(N)=2*log(N)/log(N)=2

>>8462317
That's what I thought, thanks. I wasn't sure if I was allowed to remove the lower order terms before I simplified.

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>>8462272
Hmmm... Having trouble with the open ellipsoid thing.

By the way, you helped a lot. Here's my fave wallpaper

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I must be stupid, I don't understand why the whole mass of the molecule HgO is used to calculate rather than just how many Hg is in the molecule. Shouldn't 2HgO just make as many Hg as it has? 2Hg?

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>>8462377
Nevermind. I just completed the square and got (x + 1/2y)^2 + 3/4y^2

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Not a math man, so I am struggling to find the relevant term.

Basically I have a sequence of constant track pieces, strung together to form a 2D path. Like pic related, but not constrained to right angles only.

What's that called in not-stupid words so that I can read up on it?

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Same anon as >>8462007 here. Wanted to make sure I understood the question and could give it a go before asking for proper help, but I've really no clue as to how I'm supposed to show this.

>>8462379
>Shouldn't 2HgO just make as many Hg as it has? 2Hg?
Yes, it does.
You're dividing by the molar mass of HgO because you were given the mass of some HgO
That tells you how many moles Hg there are

>>8462412
x = grad 1/2 | x|^2
use integration by parts ( divergence theorem?)

|x|=1 on the surface, and the surface area is 4/3 pi. Don't know why you don't have 1/2 though.. or what sign it should be.

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Okay, so I can find the derivative f`(x) = 4cos^2x

and I can find the roots (pi/2, -pi/2)

but when I put numbers inbetween the intervals it always equals the same thing so I can't determine whether it's increasing or decreasing

>>8462506
That's not the derivative, brainlet. Use the chain rule.

Why am I getting a different result?

I'm trying to integrate (e^t)(e^-st)dt. In my book it becomes:

1 - e^(-t(s-1))
--------------------
s-1

But with software it becomes:

e^t-ts
----------
1-s

I can see that some stuff changed, such as the sign in the exponent, and the signs in the denominator, but what I care about is that the Laplace transform will be:

something
---------------
1-s

Instead of:

whatever
----------------
s-1

That can't be right can it?

>>8462520
why am i such a retard ;_;
i always fail on small dumb mistakes

>>8462533
s-1=-(1-s)
=> 1/(s-1)=-1/(1-s)

Also: -t(s-1) = t-ts, i.e. the first form has the exponent factored, the second has it expanded.

The 1-... in the first form suggests that it's a definite integral over [0,t] rather than an indefinite integral (antiderivative).

>>8462632

>The 1-... in the first form suggests that it's a definite integral over [0,t]

Yes, it was a definite but my software can't solve that, so I figured that I could use the software to solve the indefinite and then do the other thing myself. That should work just the same right?

>>8462642
Sort of. Except that you need to calculate the definite integral over [0,infinity), and you can't just "plug in" infinity

Specifically, it means evaluating e^(-(s-1)*t) at t=infinity.

That's zero, provided that the real part of s-1 is positive.

>>8462806

I thought that all I had to do was to use the limit of of e^stuff when t tends to infinity. Is more than that needed?

>>8462816
No, just bear in mind that the limit only exists if Re(s-1)>0

The antiderivative of (e^t)*(e^(-s*t)) wrt t is
e^((1-s)*t)/(1-s) = e^(-(s-1)*t)/(1-s)

At t=0, that's just 1/(1-s). As t->infinity, it's 0 if Re(s-1) is positive or infinite if it's negative.

So the definite integral over [0,infinity) is 0-1/(1-s) = -1/(1-s) = 1/(s-1), provided Re(s)>1 (i.e. that's the region of convergence).

Is the infinite-dimensional spectral decomposition of a self-adjoint operator actually constructive?

i.e. Let [math]A[/math] be a self-adjoint operator on a Hilbert space [math]\mathcal{H}[/math] with spectrum [math]\mathrm{spec}(A)[/math]. We can write [math]A[/math] as [eqn]A = \int_{\mathrm{spec}(A)} \lambda \, P_A(d\lambda),[/eqn] where [math]P_A \colon \mathcal{B}_{\mathbb{R}} \to \mathcal{L}(\mathcal{H})[/math] is the unique PVM of [math]A[/math]. [math]\mathcal{B}_{\mathbb{R}}[/math] is the [math]\sigma[/math]-algebra of Borel subsets of [math]\mathbb{R}[/math] and [math]\mathcal{L}(\mathcal{H})[/math] the set of bounded linear operators on [math]\mathcal{H}[/math], as usual.

1) I've seen the proof that shows that [math]P_A[/math] is indeed unique, but it was an existence proof; how would I construct it?
2) What does [math]P_A(d\lambda)[/math] mean, in terms of computing the integral above? In other words, what does it mean to say that [math]d\lambda \in \mathcal{B}_{\mathbb{R}}[/math]?
3) Is [math]A[/math] *any* linear operator on [math]\mathcal{H}[/math], or is it necessary that [math]A \in \mathcal{L}(\mathcal{H})[/math] for the decomposition to work?

>>8462806

>you can't just "plug in" infinity

Why not?

lim x->Infinity: e^(21+x-Cx)

e^(21+INFINITY-CINFINITY)

No matter how big an infinity is, an infinity * C will be C times bigger:

e^(21-(C-1)INFINITY)

Several infinities can count as one infinite, because they're infinite anyway:

e^(21-INFINITY)

What is 21 compared to an infinite? Nothing:

e^(-INFINITY)

Then pick up a big number like 9999:

e^(-9999)=

And then do the same for a few numbers bigger than that:

e^(-99999999)=
e^(-9999999999999999)=

Now you can clearly see what the limit is, just use a calculator or whatever.

Dumb physics question

I understand that when you look at a collision of say a bullet and a block where the bullet becomes embedded in the block that that collision is inelastic. I understand it from numerically looking at it, but what is the intuition for it? Why isn't kinetic energy conserved when they fuse?

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Cup product???

Please explain why is it so weird? And it looks nothing like /\, exterior product, in differential forms, which are supposed to make de Rham cohomologies a graded ring as well. That's very strange.

Anyone knows why it is the case?

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>>8463084
Oops wrong pic

>>8463084
Ah, wait, I think I know the answer.

>>8463043
The kinetic energy ends up as heat.

Consider a collision involving a bean bag which barely bounces. During collision, the "beans" (or whatever is inside it) move around, converting most of the energy to heat via friction.

Something similar will tend happen to an extent for any real (i.e. non-ideal) material.

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Explain the question simply and what method do I go about to solve this

>>8463178
Any x approaching 0 will make the first f diverge since 1/x^2 will blow up faster than x will shrink. Just pick y=0 for convenience.
In the second f you can't have y=0 because it's in the numerator, but to avoid having to deal with the sum in the denominator, you can just pick x=y.

If the torque is perpendicular to the angular momentum, why is there only a change in the direction of the angular momentum and not also its magnitude?

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Pls
Is this right?

I measured two values M1 and M2.
The addition of both is Mtotal, an indirect measurement (calculated).

I tried to calculate the error of Mtotal from the error of both M1 and M2.

Tell me. Is the result right?

>A weight lifter lifts a 290-N set of weights from ground level to a position over his head, a vertical distance of 1.65 m. How much work does the weight lifter do, assuming he moves the weights at constant speed?

I know that since the velocity is constant, acceleration is 0, and so net force is 0. Therefore F * d = 290 * 1.65 = 478.5 J.

My question is, if he's applying a force equal to that of the set of weights, how is it lifting?

Help me /sci/

How do I show picrelated ? It's used to show that J2 is multiplicative, so obviously I can't use that.2 is the second Jordan totient fuction

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>>8463828
forgot pic

>>8462384
https://en.wikipedia.org/wiki/Path_(graph_theory)

Or for the more general topic:

https://en.wikipedia.org/wiki/Graph_theory

>>8463838
just use a combinatorial proof
the left hand side is just a partition of n^2 into the number of elements of each order

>>8460476
You're trying to factor it into the form (a + b)^2.

Expanding that gives:
a^2 + 2ab + b^2

Now you need to identify these terms in the expression you're given.

Two of them should be something squared (let's call those somethings a and b) and the other should be 2 times the product of a and b.

You were given:
1/2 + x^2/4 + 1/(4x^2)

So you just try two of them as the something-squareds and see if the remaining one is 2 times the product of the somethings. There's only 3 combinations to try out.

Hint: They're usually going to give you something that reduces nicely, so the 1/2 term is not likely the something-squared, since that would give 1/sqrt(2) as the something.

If I were to integrate a fuction wrtx where for
0 < x <1, why do we take limits of 1 and 0 if the x values can't equal these values

Given [math]ax=x^2[/math], is [math] a=x[/math] iff [math] x\neq0[/math]?

>>8464008
yes because it rearranges to x(x-a)=0

unless you're working in a ring with zero divisors, then there are exceptions

>>8463892
Thanks. I'm fucking retarded

>>8463988
What's the closest real number to 1 that isn't 1? This is essentially what your problem breaks down to.

>>8464041
So essentially it's limits of 0.9999.. and 0.0000..1

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i've got the MATLAB plot in pic related
how do i get the axes to show more digits?

>>8464090
also:
i can't seem to zoom in or out on this particular plot. i plotted some other curve to check whether i could zoom in on that one, and it did work. hlep pls?

>>8462094
>>8462115
As far as I know, it does not follow f' is strictly increasing from the fact we know for all x in (a, b), f''(x) > 0. How then do I should it is strictly increasing?

>>8464054
No, the limits are 0 and 1.

What exactly is a level surface?
How exactly is a surface transformed into a level surface?

I understand that [math]F(x,y,z) = c[/math]

But I can't understand it as a concept, can anyone help out?

What is the intuition behind cosets? In particular, why is the equivalence relation used to generate them defined the way it is? It just doesn't seem very natural to me. I understand what an equivalence relation is, and I understand they [cosets] are equivalence classes and the elements of the quotient group G/H, its just not obvious to me why we define cosets as such.

Here is the definition from my book. Let H < G. Then for x,y in G,define the relation x~y <--> xy^-1 in H. The equivalence classes are then Hg = {x in G: x = hg, h in H}.

To my understanding, given a group (G, *), and H < G, we get our cosets by spamming everything in H by some g in G. The resulting structure is a coset. Now it makes sense that if g in H then the resulting coset is H, but whats the intuition behind doing the group operation to the elements of H with other elements in G but not in H? Or is it common in higher math to just try doing things like this because we can? Any insight would be most, most appreciated.

>>8464041
>what's the closest real number to one that isn't 1?
>chooses 1

How?

>>8464171
>What is the intuition behind cosets?
you can think of each coset as a 'translate' of a given subgroup

>but whats the intuition behind doing the group operation to the elements of H with other elements in G but not in H?
when you do it with every element from G the cosets partition G

>>8464181
There is no real number which has those properties hence you're forced to choose 1 as the only sensible limit.

>>8464171
>and I understand they [cosets] are equivalence classes and the elements of the quotient group G/H
it's good to remember this is only when H is normal, otherwise there's no group structure on the cosets

>>8463193
>>8463178

Still not sure how to solve the problem

>>8464203
it literally tells you how in the hint brainlet

>>8464183
I think I see what you mean by each coset is a translate of the given subgroup. If one thinks of the integers as magnitudes on the line, and addition is concatenating them on the line, then the result of will be the corresponding magnitude. So give a subgroup H and g in G, Hg is simply concatenating each element in H with g. Is this what you mean by a translate?

>>8464186
Ah yes, thank you. I will keep this in mind?

>>8463178
Try finding the path when it comes down to the limit.
The limit does not exist for the first one, hence it's not continuous, you get [math]\frac{(-1)^{\frac{1}{2}}}{m}[/math]

How do I use Latex on /sci/?

>>8464213
Here ya go.
[math]\frac{(-1)^{\frac{1}{2} } }{m}[/math]

>>8464215
Read the fucking sticky

>>8464219
What?

>>8464208
by translate i mean like:
if G = integers with addition, and H = {multiples of 3}
then:
0+H ={..., -9, -6, -3, 0,3,6,9,...}
1+H={..., -8, -5, -2, 1,4,7,10,...}
2+H= {..., -7, -4, -1, 2, 5, ...}
hitting the coset H with any group element g sort of 'moves you around' to another part of the group, depending on what the remainder of g is when you divide by 3

if you were to think of a vague 'picture' of a group, then taken together the cosets cover the group and cut it up into pieces (so G is the disjoint union of the cosets)

>>8464220
The /sci/ sticky contains instructions on how to use LaTeX on /sci/.

>>8464223
I'm the other guy you replied to.

>>8464225
Oh right.

/sci/'s LaTeX has some problems; unless you put spaces in between certain characters, it won't show up properly. For example if it contains a }}, you need to make it } } instead.

>>8464229
Oh alright thanks

File: Screenshot from 2016-11-08 18:54:16.png (32KB, 669x294px) Image search: [Google]

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Help my brain.

How do I do any of these beyond ii)?

>>8464348
first one is easy just choose the order dydx and you'll solve it easily
second one you draw the boundaries and change the order to dydx
same for the third, draw and then change order to dxdy

>>8464221
Awesome, this helps tremendously. Thank you!

>>8464352
I didn't know you could fuck with the boundaries like that. Thank you, and thank Paul's Notes

>>8464369
Be careful about where the rays enter/leave though, otherwise you boundaries will be wrong and you'll get a wrong answer

Is it true that f(x) = |x|^3 = {x^3 if x > 0, (-x)^3 if x< 0?

>>8464439
yes

>>8464448
thank you. is it true f(0) does not exist since it is undefined for the component function |x| by the definition of derivative of function composition?

>>8464450
>f(0) does not exist since it is undefined for the component function |x| by the definition of derivative of function composition?
no idea what you're talking about, |0|=0 always

How do I know what is F and what is G in a convulution in the Laplace thing? If I have:

L{ 7*t^2 }

I know that the functions are 7 and t^2, but does it matter which one is G and which one F or it works either way?

>>8464540
Is that a convolution or a multiplication?

For a constant, there's no difference; it's just 7*L(t^2).

Also, convolution is symmetric; f*g=g*f.

Why is cat fur so soft and nice?

>>8458969
>>8458925

Why is it the area in between the two curves? And nothing outside?

File: cubicles.jpg (46KB, 741x179px) Image search: [Google]

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Anyone have any hints for either of these?

I'm having a difficult time visualizing it.

i have to calculate the condition number when evaluating some polynomial in some x. what the hell am i even supposed to do here?

>>8464700
#3 is a graph-colouring problem, but it's not planar.

Two "cubicles" share a common vertex if they're adjacent (including diagonally). So the corner cubicles have 7 neighbours (2x2x2 block), the edge cubicles have 11 neighbours (2x2x3), face centres have 17 neighbours (2x3x3), and the centre has 26 neighbours (3x3x3).

In #4, the "no cubicle with 3 red faces" rule requires that the same-colour faces form 2 "C" shapes, i.e. colour 2 opposing faces red, along with one of the other faces. I.e. you can't paint the 3 faces around one corner red.

The ones which don't have both red and blue faces are the 2x2 blocks in the centre of each face, the 2x1 blocks in the centre of edges between 2 same-colour faces, and the 2x2x2 block in the interior (which have no painted faces).

The ones which do have both red and blue are the 2x1 blocks in the centre of edges between faces of different colours, and all corner blocks.

>>8464782
The condition number of a function at a point is x*f'(x)/f(x). For a polynomial, it asymptotically approaches the degree as |x| gets large.

Note that the general form is equal to
(d log(f(x) / dx) / (d log(x) / dx)
i.e. it's the slope of a log-log plot of the function at a given point.

>>8464816
>The condition number of a function at a point is x*f'(x)/f(x).
what if x is the point where f(x) = 0?

What happens if I have a matrix where the determinant is nonzero and the nullspace is nonzero? Are the columns independent or not? Did I fuck something up?

>>8464859
Then it's undefined.

Note that for a log-log plot, neither x nor f(x) can be zero or negative.

The condition number is a measure of whether a function is well-conditioned or ill-conditioned. Specifically, the ratio of relative error in the function's value to that of its argument.

A larger argument means a larger absolute error for a given relative error. Higher slope magnifies the absolute error. A value near zero means a larger relative error for given absolute error.

All of them being true at the same time make a function particularly ill-conditioned. The classic example being arccos(x) at x=1 (as x tends to one, the slope tends to infinity and the value tends to zero). Its condition number is x/(sqrt(1-x^2)*arccos(x)), i.e. both terms in the denominator tend to zero as x->1.

>>8464922
That's impossible. The determinant has to be zero if the nullity is non-zero.

Note that numerical software generally uses a tolerance (epsilon) value when calculating rank and/or nullity, because otherwise square matrices would almost inevitably be considered full-rank, if only because of rounding errors in the calculations.

(Essentially, such calculations involving comparison with zero, and testing whether a floating-point value is exactly equal to zero is usually ... unwise).

>>8464943
> Then it's undefined.
... or infinity, depending upon your perspective.

File: help.png (31KB, 683x112px) Image search: [Google]

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First time learning Abstract Algebra using Topics in Algebra by Herstein. Can someone explain to me why the intersection is the null set?

If the directional derivative does not exist at a point, must this mean that the function is not differentiable at that point? I think this is true but I am not 100% sure.

>>8464956
The intersection is made of the real number that are higher than all rational numbers. There are no such real numbers (Because Q is archimedian)

>>8464451
whoops, sorry that meant to read as "is it true f'(0) does not exist..."

>>8464981
I see, thanks anon.

>>8464090
Show code.

every cicle is a path?

File: simplify.png (29KB, 560x123px) Image search: [Google]

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How does it become -h^3/6?
That seems like an approximation at best to me.

>>8465266
x_1^3/3-(x_1+x_0)x_1^2/2+x_0x_1^2-x_0^3/3+(x_1+x_0)x_0^2/2-x_0^2x_1
=(x_1^3-x_0^3)(1/3-1/2)+x_1x_0(x_1-x_0)/2
=-(x_1^3-x_0^3-3x_1x_0(x_1-x_0)/6
=-(x_1-x_0)^3/6=-h^3/6

>>8464994
if these are al
[f(h)-f(0)]/h
= [|h|^3/h]
= [ (±1)|h|^2]

taking the limit as h goes to 0 gives you 0 so the derivative is 0 at x=0

Could someone help me with this proof?

Consider f such that f(0) = 0 an f''(x) <= 0 for all x > 0. Then, a >= 0 and b >= 0 implies f(a + b) <= f(a) + f(b).

Here is what I have:
Let f be defined as above, a > 0 and b >= a. Then by the Mean Value Theorem there exists c in [0, a] such that

f'(c)(a - 0) = f(a) - f(0) => f'(c)(a) = f(a) - 0 = f(a)

Likewise there exists d in [b, a+b] such that

f'(d)((a+b) - a) = f(a+b) - f(a) => f'(d)(b) = f(a+b)

Not sure exactly where to go from here, but I'm pretty sure I need to use the definition of a subadditive function, which says, Given a function f:R->R is a subadditive function iff f(x + t) <= f(x) + f(t), for all x,t in R.

Any help would be most appreciated

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>>8464793
Would the smallest number of colors be 8? I got that the smallest way to do a 3by 3 square is with four. Theres no way to reuse a color for the next layer so I would need four new colors, but then I could repeat this layer for the top 3x3 square

>>8465314
wow i can't believe i had such a hard time with that.
thanks anon.

File: Untitled.png (2KB, 196x60px) Image search: [Google]

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What is the limit as t tends to infinity? I don't think it exists.

File: dota waifu.png (3MB, 2282x1259px) Image search: [Google]

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>>8454755
I saw some kids cheat in one of my higher level engineering classes, should I send an anonymous email to the professor? It was pretty fucking blatant and I'd think it be bullshit if those chuckle fucks got a better grade than me in the course by doing piss all.

>>8460365
>>8460310
Uncanny

>>8465565
0

>>8464958
Yes.

>>8465357
> Would the smallest number of colors be 8?
I'm not sure. Clearly 8 is sufficient, but It's not immediately obvious that it's necessary.

>>8465565
It's zero, provided that the real part of s is positive.

For any integer n, (t^n)*(e^-t) tends to zero as t tends to infinity.

>>8457145
Depends how you use it.

Didn't post this question here because I think asking for a problem to be solved is too much, but I hope you don't mind me cross-posting it just in case I can get the attention of someone who wants to help.

>>>/wsr/218280

I'm trying to solve this

[math]y'' + 2y' + 2 = 0[/math]

and I went to solve the quadratic [math]m^{2} = 2m + 2 = 0[/math]
but I'm stuck here because that doesn't solve well. Maybe I'm just an idiot. I only learnt this stuff today but I could do all the other questions on it.

How can I take the partial derivative of something like this:

[eqn]
\frac{\partial}{\partial \alpha}|\mathbf{X}\alpha\mathbf{I}_n\mathbf{X^T} - \sigma \mathbf{I}_m|
[/eqn]

where [math]\mathbf{X} \in R^{m \times n}[/math], [math]diag[/math] is a diagonal matrix, [math]|\mathbf{X}|[/math] is the determinant of [math]X[/math], and [math]\mathbf{I}[/math] is the identity matrix? Same question for the partial derivative wrt [math]\sigma[/math] if anyone knows

>>8466216
d/dt e^at = a.e^at

Note that complex values of a are fine (they turn into sin/cos).

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>>8463178

In response to my original question can any tell me with reason if my working is correct?