/sqt/ - Stupid Questions Thread

What is the significance of C-Squared and how does it relate to the energy-mass equivalence?

Why is the total energy of a system equal to its mass + the speed of light squared?

And why does total energy/c squared equal the total mass of a system?

How does light pass through a prism and what slows down it's speed to an outside observer?

Don't you dare say it's scattering or absorption, because, if that's the case, then explain why the light stays in a straight line. No bullshit.

>>9154203
>>9156228
Thank your very much ! Alpha = 60°

Once upon a time I ran across a website that had a bunch of mathematical questions ranging from "Easy" to "Hard". Where most if not all of them needed some knowledge of programming in order to find the answers to them.

My question is does anyone know of which website it is and what is the website?

Can someone clear up additive vs nonadditive genes for me? I'm getting multiple sources contradicting each other. From my understanding it's:
Additive---------
-works with other genes to build up trait (polygenetic)
-both forms of the allele (AA or aa) most be there (not can be dominate)

Nonadditive---
-can have a epistatic affect
-when the dominant allele over takes the recessive allele (dominate)

Does fecal matter?

Which grows faster, n^x or nCr?

>>9157077
Put nCr in terms of the gamma function

>>9157041
sounds like project euler

When our ancestors started losing their fur, why were they still mated with? Wouldn't the furless homos have been outcasts?

>>9157077
I don't get what you mean. n Cr what?

n^x will grow indefinitely as x increases. n Cr x will decrease when x starts approaching n.

Alright, so every time I think I have a handle on how linear algebra concepts work, some problem comes along that destroys that perception. Here this problem that first asks to show why Ax=b does not have a solution for every possible b. Easy enough, row reduce the augmented matrix associated with this equation and point out the inconsistency.

What I don't understand is the second part, "describe the set of b for which Ax=b does have a solution". What I ended up getting (for the row reduced matrix) was :
[ 1 1/3 b1/3
0 0 3b1 + b2]
The solution says "the set of b for which the equation is consistent is a line through the origin - the set of all points (b1,b2) satisfying b2 = -3b1".
I'm not understanding this answer. I know 3b1 + b2 has to be 0, but I don't know why we are solving for b2.

>>9157077
Do you mean what grows faster,
[math]n^{x}[/math]
or
[math]\frac{x!}{(x−n)!n!}[/math]
when n is kept constant and x varies?

>>9156913
How do you find the length from one point to a nother in a parabola Not from one point to another from a straight line but across the parabola?
Is there an equation for it?

>>9157059
Nevermind. I figured it out. Although, I'm surprised no one replied.

>>9157147
it's called arc length and is usually covered in Calc 2 courses. Have a read if you're ready for it:

http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

>>9156928

It's the speed of light squared, and it relates the energy mass has simply by existing i.e. all possible energy than can be extracted from purely mass

it's not.

it doesn't.

>>9157132
Correct.

>>9157111
Let n >> x then

>>9157211
looks like n^x grows way faster.

Why are we spending so much money and effort to fix global warming.
It is a self correcting problem
Humans make to much co2
Earth can't support the human population
Human population declines
Humans generate less co2

>>9157355
Because humans don't want to die?

>>9157376
The evidence dose not support you

what the fuck does it mean to "prove analytically"?
i've never done a proof before pls help

>>9156913
how do I get good at control theory?

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>>9156913
>differential equations
This is probably simple, but I just can't figure out why the highlighted expressions are equal.

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>>9156913

is the photoelectric effect a cause of ionization? this seems to say so http://ecetutorials . com/photo-electric-effect-and-photo-ionization/

how?

isn't it the case that the electron being hit stays in the atom, just at a higher energy level? and then emits a photon with caracteristic energy to descend back?

am i missing something?

>>9157490
Oh wow, I understand it now. Product rule.

>>9157493
My physics is rusty, but I got this from a quick search:
>"Pulses of radiant energy, such as X-ray and gamma-ray photons, can eject electrons from atoms by the photoelectric effect to cause ionization."
>"In the photoelectric effect, light incident on the surface of a metal causes electrons to be ejected."
It's got something to do with the work function of the metal or something.

>>9157497
hmm. so then what's the difference between it and the Compton effect?

>>9157499
>>9157497

maybe just the energies involved?

or the energy of the outgoing photon in the case of the photoelectric effect is characteristic to the atom being ionized and in the case of the Compton effect it isn't?

[math]\lim_{x \to 1} \frac{x^2+x-2}{x-1} = 3 [/math]
I’ve been finding deltas in terms of epsilon for a little while, and all of them seemed obvious until I tried this one. I was getting (correct) answers of delta equaling some simple fraction of epsilon, so in this case I figured that they would equal each other. Apparently, though, delta is *less than or* equal to epsilon here. Does anyone know why the answer has that extra condition?

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is this correct? if not plz help. ty

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>>9156913
guys I feel like a complete and utter brainlet in basic probability... could you help me solve this for P(A)? please show the steps so I could figure out where I got lost (tried using set theory algebra but got stuck).
the problem is in pic related.
thanks in advance!

>>9156928
C^2 is there for the unit conversion
We know energy and mass are equivalent because when a body of mass for instance exerts radiant energy it also lose mass, and when a body of mass increases velocity it's kinetic energy increases and so it's mass does as well.

>>9156933
Light always moves in a straight line, it's angle however can change and that is waht happens when it scatters. The light beam enters the prism an than scatters into dofferent angles and thereby different wavelengths.

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How can Neanderthal have reproduced with homo sapiens and/or cro-magnon if they were different species ?

By the way, can eskimos and aborigenes have fertile offspring ?

Why doesn't the minimal polynomial need to exist when T is a linear operator on an infinite vector space?
I couldn't understand the very few examples that I've seen on Google.

>>9157382
It means to prove with rigorous mathematical formulations of the concept, rather than construct a geometric interpretation. For example, a parabola with the origin as its center can be described as increasing on either side of the origin exponentially as x approaches infinity. Or you could just give an analytical solution that describes it and not bother with the geometry of the curve, and say y = x^2 and throw out any geometric description, it's completely described by variables and numbers.

can i use le hopital when the limits result in 1/0, and not in 0/0 or infinity/infinity?

>>9157815
>>>/pol/

What is the difference between the inner product and the dot product? How is the inner product a "generalization" of the dot product?

>>9157953
no, depending on whether 0 is being approached from the left or the right, it would be -∞ or ∞ respectively

>>9157631
Factor the quadratic anon.

>>9158091
>What is the difference between the inner product and the dot product?
inner product is a map taking two vectors to a field element which satisfies certain axioms

dot product is a particular function that satisfies those axioms, so it's an inner product

>>9157894
thanks so much buddy

>>9157738
seriously nobody?

Can [math]\sqrt{5}[/math] be shown to exist?

>>9158434
Fuck you.

>>9158450
Excuse me?

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>>9158434
It can be shown that [math]\sqrt{5} \not \in \mathbb{Q}[/math]. The existence of a set [math]A[/math] such that [math]\sqrt{5} \in A[/math] is currently an open problem.

>>9158434
[math]\sqrt{5} [\math] has [math]x^2 -5[\math] as its minimal polynomial over [math]\mathbb{Q} [\math]. This polynomials is irreducible, so [math]\sqrt{5} [\math] belongs to [math]\mathbb{Q}[x]/(x^2-5) [\math]

>>9158472
Brainlet. Quadratic reciprocity. The square root of 5 exists in many Z/nZ rings.

>>9158472
I see.
>>9158505
This doesn't look like a proof.
>>9158508
>The square root of 5 exists
Prove it.

>>9158519
Consider the field Z/11Z.
Here 4^2 = 5. Therefore the square root of 5 is 4.

>>9158524
Prove that it is a field, prove that 4^2 = 5.

>>9158537
If you haven't even studied Z/nZ rings then I recommend finishing 8th grade before you post opinions about math

>>9158541
>Z/nZ rings
Prove that Z/nZ is a ring for arbitrary n.
>before you post opinions about math
What are you even talking about? I asked a simple question. If you don't have the expertise to answer it, then just don't even reply.

I like the idea of burning things with sunlight and a large converging lens.
However, I don't like the fact that the burning point is a set distance away from the lens.

Is there any reason why I couldn't place a diverging lens just before the focal point or a converging lens just after it, and collimate the cone of sunlight into a "beam"?

>>9158550
Dude, all you are asking for is on google. Even wikipedia tells you all you need.

>>9158568
I don't use the websites you mentioned though.

>>9158569
Then get a book on elementary number theory

>>9158574
Which book do you recommend?

I have a question regarding evolution/genetics.

How is it that when a woman and a man have a kid, the 2 genes manage to mix so perfectly? Since the potential genes on the mother's side and the father's side can be so different, how can they come together so perfectly to form a healthy child? For example, when you take the combined genes for bone structure, why are there relatively few deformities?

Or take something like skull size and brain capacity, is it possible to get a slightly larger brain from one side of the family, and a skull incapable of adequately housing the brain from the other side?

I can notice in my hands that one hand resembles my mothers, and the other my fathers, and they work but theyre relatively crude parts of the body compared to extremely delicate things like eyes, ears, brain, heart, nerves, etc. work so well based on randomization?

My understanding of this subject is primitive and im studying in a completely different field, but can anyone give me some sort of normie answer?

tldr:
Why isnt everyone completely deformed based on the randomization of genetics?

Is it advantageous for an actuary to have a Master's degree or doctorate? If so, when (relative to accreditation as ASA and FSA)?

Is there a name for this sort of flawed reasoning?

Someone flips a coin 10 times, notes the results, and since the probability of this exact sequence coming up is 1/1024, the fact that this sequence came up should be regarded as an extremely unlikely occurrence. Obviously the error is that some sequence of coins had to come up, and the person flipping the coins would have made the same statement no matter what sequence came up.

>>9158675
where exactly is the flaw supposed to be?

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I know I could just plug it into wolfram, but how would you figure this out by hand other than just multiplying it out?

>>9158599
My professor used Niven. It's pretty good. I learned all from my professor so I have never actually read a full elem. number theory book, I have just skimmed some, but if he says its good then its good

>>9158684
Binomial theorem.

>>9158684
I think that's simple statistics.
(b) and (c) should be obvious.

It's (1+x^3 + x^5) * (1+x^3 + x^5) * .... * (1+x^3 + x^5)
Which options are there to arrive at a*x^3?
1*1*...*1*x^3
1*1*...*x^3*1
...
1*x^3*...*1*1
x^3*1*...*1*1
In total 15
Similarly for (d)

>>9158699
Aw makes sense. So we are really just thinking about how it could be done and then counting the permutations. Interesting. Thanks!

>>9158675
I would describe that as a misinterpretation of a probabilistic event. It's not unlikely compared to the probability of any other sequence of coin-flip results. So if there isn't anything else involved but the flipping of coins, saying "wow that was really unlikely" isn't a meaningful statement.

Now, suppose someone predicted that exact sequence in advance, and it occurred. THEN you could say "wow that was really unlikely," and it would be a meaningful statement. Namely, given the null hypothesis that the actual outcome will have a 0 correlation with the predicted outcome, a correlation of 1 would be evidence that the predictive mechanism is real.

Alternately, suppose someone won the lottery. Because winning the lottery is significantly less probable than losing, then it would also be meaningful to say "wow that was really unlikely" both because of the comparative probability of a win to a loss, and because of the actual reward involved.

>>9156913
I want to get my hands on some quality lunar tools the astronauts used during the moon program, where could I go to get an exact replica?

Looking for something that is functional and as close to flight hardware as possible

>>9158142
I did...? That's how I got my original answer of delta = epsilon. I don't see how that explains it.

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>>9156913
Guys what the fuck

Euler's formula says for any planar connected graph, the number of vertexes plus the number of faces minus the number of edges equals 2

v + f - e = 2

What about this? Am I literally retarded? It equals 1 here

>>9158786
Oops I found it out. The external of the graph counts as the "infinite face" lol so F=6 not 5...

>>9158802
what are you confused by? show f(a/b)=0 implies a divides c_0 and b divides c_n

If I have 2 linear trasnformations [math]A, B[/math] and a scalar product [math]<,>[/math] such that [math]<Ax,By>=<Ay,Bx>[/math] for all [math]x,y\in \mathbb{R}^n[/math] then is is true that the scalar product banishes everywhere?

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How exactly would I show that this is true?

I mean isn't it just trivial. If you reduce a polynomial of power two or three you will always have a polynomial of power 1 which is always solvable for a rational number?

Is that enough proof?

>>9158892

use [math]\langle \ \rangle [/math]

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What did he mean by this?

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Gonna try here before I make a thread about it.

I'm doing to calculate the spectral kernels of a Constant Q Transform by calculating the temporal kernals, then doing an FFT as in this paper:
http://academics.wellesley.edu/Physics/brown/pubs/effalgV92P2698-P2701.pdf

My MATLAB code is at https://pastebin.com/kqG69fYJ

I'm stuck on the "calculating the temporal kernels" part. I'm trying to do it with the centered Hamming function and complex exponential as shown in Eq. 7, but my temporal kernels don't look anything like the authors, which increase in frequency and become less spread out in the time domain with increasing kernel number.

I noticed that with my current setup, every other complex exponential is simply 1. Is this part of the problem, or is there something else I've overlooked?

Thanks in advance.

Lost /x/fag here trying to not die.
Trying to refine Potassium Carbonate into Angel Water. The method I'm following says to use a glass dish but also mentions that the substance is corrosive enough to etch into the glass. Are there certain types of ceramic wear that it won't react with, or do I just stick with the glass.

>>9157738
not enough info

>>9159027
>Angel Water.
What's this?
If you're playing with chemicals just to make bullshit magical potions, then please kill yourself.

>>9159057
Angel water is a strong alkaline substance that you get from exposing potassium carbonate to ambient moisture.

Hi /sci/,

Got a question here hopefully some of you guys can help to answer.

I'm currently working on university computing math and I'm told to proof (p ^ q) -> (p v q).

I more or less have it worked out, just need to sort out 1 tiny question.

In Logic, the commutative law states that (p v q) is logically equivalent to (q v p), however it does not state whether it applies for statements with more than 2 atomic propositions.

can you swap (~p v ~q) v (p v q) around so that it becomes (~p v p) v (~q v q) using the Commutative Law?

I know that they are logically equivalent, but what law can i use to swap the atomic propositions if I can't use commutative law?

>>9159090
>proof (p ^ q) -> (p v q).
Sorry that makes no sense

prove that? That is not a true proposition

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>>9159090
Can anyone help me out as to how I would read these kinds of engineering drawings?

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>>9159150

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>>9159156
I know you would line them up but alot of it just seems like ADHD gibberish so many different section shots

>>9158564
Of course not. You can put an infinite amount of converging and diverging lenses together, but you'll lose some power as light changes between the glass and air. The only thing I'd say is you don't know where the rays from the diverging lens are going.

>>9158892
>If I have 2 linear trasnformations A,B and a scalar product <,> such that <Ax,By>=<Ay,Bx> for all x,y∈Rn then is is true that the scalar product banishes everywhere?
no, consider A=B=identity

>>9159193
fugg I forgot to add a minus sign. I think I solved it though.

>>9159149
Are you kidding? It's literally a 3 liner constructively, which means it's valid classically as well.
Assuming "^" is "and", "v" is "or" and "->" is implication.

Let's say you started running a big software company, and many of your competitors are amoral assholes.
What kind of antidote/antipoison would you always keep at hand in case if some of the more coward competitors try to poison you?
Also, what other precautions would you take? What medical checkups are a must?

Asking here because this is somewhat med. science related.

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Platintum (IV) Chloride Azanide

Why do the the hydrogens on the azanide group point toward the platinum atom?

>>9158550

It's a ring by definition, because it has group structure under addition and is closed under multiplication. the n can't be arbitrary though, must be integers. >=1 but Z/Z is isomorphic to the identity group so we just start with 2

>>9159090
input (p & q) -> (p | q)

at https://programming.dojo.net.nz/study/truth-table-generator/index

>>9159045
are you sure? how did you understand this? this is exactly as written in the textbook

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I have a Calculus exam in exactly one weeks time that I haven't started studying for at all

What's the best way to learn 7 weeks of maths content? My usual strategy is just to do questions over and over until I get them right.

Is there are more intelligent way to study for a maths exam?

>>9156913
Can someone please give an example of a practical DIY project - electronics, computer, mechanical, that you need to know linear algebra for ?

>>9159027
>>9159082
>>>9159057
>Angel water is a strong alkaline substance
It's just KOH, you might as well buy it.

K2CO3 + 2 H2O ----> 2 KOH + H2CO3 ---> 2 KOH + H2O + CO2

And no, I don't think it will react with glass nor ceramic at all.
The only thing that can react with those two is hydrofluoric acid.

>>9159149
Sorry not proof, i meant proof its a tautology.

>>9159392
Seems odd to me as well. Unless maybe you consider the interaction between the hydrogens and the d orbitals of the platinum perpendicular to the plane. (you know, the hydrogen bond bridge or whatever) Metallorganic is not really my field, I just did an exam.

>>9159607

see >>9159431

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What are some good budget laptops? Also are their any good ultrabooks for under $300? I'd ask in /g/ but everyone just circlejerks thinkpads.

Is the following equality true? [eqn]\{\textbf{x}\in l^\infty : \lim_{n\rightarrow \infty} x_n \text{ exists}\}=\{\textbf{x}\in l^\infty : |\lim_{n\rightarrow \infty} x_n| < \infty\}, \text{ where } l^\infty=\{\textbf{x}\in \mathbb{R}^\infty : \sup_n|x_n|<\infty\}[/eqn]More precisely I wonder if "exists" in the first set means that the limit of the sum of components is finite? If not, exactly what does "exists" here mean?

Please explain like I'm mentally retarded

Solve
[math]\frac{d^2y}{dx^2} = e^x \quad \textrm{given} \quad y(0) = 0, y(1)=0 [/math]
Using the Green's function method

>>9156913
Can I do an extended fast and still study efficiently?

>>9159781
yes

Would a pure hydrogen bombs be against the nuclear non proliferation act of 1978?

>>9159818
y'' = e^x with y(0) = 0, y(1) = 0 with green's function
fuck that, just integrate it
y' = e^x + C_1
y = e^x + C_1*x + C_2
C_2 = -1 , C_1 = 1 - e.
y(x) = e^x + (1 - e)*x - 1.

What does it mean to write a function as a product of irreducible factors over Q?

For example I have:
(x+x^2+x^3+x^4)^2

which can be worked out to equal

x^2(1 + x)^2(1 + x^2)^2

This is a product of irreducible factors, correct?

>>9157076
Yes

Just testing if latex works here

[math] f(x) = a^{x} + cos \pi [/math]

>>9159982
[math] f(x) = x^{2} \\ f'(x) = 2x [/math]

Given a weighted, undirected graph G with nodes and edges.
[math] R_j [/math] is the rank of the edge j in the sorted list of edge weights.

What is the rank? When I google it, it shows this result: "rank r of an undirected graph is defined as the rank of its adjacency matrix."
This doesn't help.
Or should I understand the word "rank" more literally here? If i sort the edge weights, than say the edge with the biggest edge weight has rank 1 (or zero i guess)?

So the reason we think the universe is 13.something billion years old is because that's how old the first observable light we've found is?
Doesn't that imply that it could be older but we just haven't seen light that old yet?

>>9159988
The rank of a matrix is the dimension of the vector space it can cover. Quick example:
[eqn]\begin{pmatrix} 1 & 0 \\ 0 & 0\end{pmatrix} \,\times\, \begin{pmatrix} x \\ y \end{pmatrix} \,=\, \begin{pmatrix} x \\ 0 \end{pmatrix}[/eqn]
That matrix has a rank of one because you can never escape the vector line [math]\mathrm{Vect}_{\mathbf R} \begin{pmatrix} 1 \\ 0 \end{pmatrix}[/math] with it.

>>9159988
I suspect it would be the latter.
Given the wording you posted, the rank of the adjacency matrix doesn't seem to be of any use.
What is the rest of the question?

>>9156913
I'm having troubles with this problem. Can anyone help?


Find f ' (a) if f(x) = Sqrt(1-2x) using the limit definition of the derivative.

I can't figure out how to further simplify at this point

lim h - > 0 Sqrt((1-2h+2a))-(1-2a)) / h

>>9160092
sorry its

sqrt(1-2h-2a) - sqrt(1-2a) / h

>>9160099
Please learn LaTeX.

>>9159871
yes
the detonator of a fusion bomb is a fission bomb

I really suck at solving physics problems and the textbook (calc. based serway) examples are fucking easy.

Should I get the Schaum 3k Physics Problems and the College Physics?

I dont like physics, I just want to get A

a is orthogonal to b and c
b is not a multiple of c
is b orthogonal to c?

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>>9156913
Ok this probably is a stupid question (see pic related)
answers for part a) are non-linear, order 1, and separable
How do you do part B? I get x=tan(y)+c but its wrong and the plus sign is not recognized by the website

>>9160304
>is b orthogonal to c?
not enough info to determine

>>9160305
Correction: I get arctan(y)+c

>>9160309
What else do I need to know?

>>9159903
The whole point is to use Green's function, I know how to integrate.

>>9160319
consider a=(1,0,0) which is orthogonal to b=(0,1,0) and c=(0,0,1)
b isn't a multiple of c, and b is orthogonal to c

now consider a=(1,0,0) which is orthogonal to b=(0,1,0) and c=(0,1,1)
b isn't a multiple of c, and b is not orthogonal to c

>>9160305
>I get x=tan(y)+c
>+c
>in an initital value problem

>>9160336
>>9160336
Anon you just explained it beautifully and I got it right, thank you

>>9160170
A pure hydrogen bomb isn't detonated by fission.
(they don't exist yet)

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Has anybody looked at the Orch OR theory of consciousness? What were the main takeaways?

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>Consider two real numbers x, y. Prove that if xy = 0 then x = 0 or y = 0.

By contrapositive: [math]x\neq 0 \land y\neq 0 \implies xy \neq 0 [/math]

Since x, y are non-zero, xy will have a unique non-zero product. Thus by the contrapositive, [math]xy=0 \implies x=0 \lor y=0[/math] is proven true.

QED?

This seems too simple.

>>9160402

"unique non-zero product" is a handwave, not a real explanation unless you've already proved this.


Here's a better way: Suppose xy=0.

Case 1: y=0. Then easy, we have that x=0 or y=0 is true.

Case 2: y =/= 0. Then multiply xy by the multiplicative inverse of y, 1/y. So you have xy(1/y) = 0(1/y) ==> x = 0. There you go, QED by proof by cases

>>9160423
doesn't proof by cases only work when you have statements [math]P\lor Q[/math] on the left hand side of the implication?

>>9160434
No. You can think of it as if you have two possibilities for xy = 0 and then you get to the conclusion that either one or both of them are 0.
It's kinda the same if it was the opposite, but it'd be more clear for you to know what are the cases.

Is it possible for a clone of a straight person to turn out gay?

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Brainlet here, not sure if I did this right.

I-I just plug in the 7 for X r-right.

>>9160478
Ah, I see. Thank you.

>>9160500
you cant just throw away that negative 1

>>9160528
So, 10-i(sqrt2)

What's the part of the equation called that must be solved in order to find the answer? Ex. 12/4+15=x
What is the technical name for the equation of 12/4 within the bigger equation of x?

>>9160550
the numbers can be thought of as being multiplied to a polynomial of degree zero.

>>9160544
is that a real number?

>>9159528
I'm not a STEM major, but this is what I did.
Let a = intersection of complement A and complement B. Let b = intersection of a and complement b. Let c = intersection of a and b. Let d = intersection of complement a and b. Draw a venn diagram to see if you know what I mean.
We know a+b+c+d=1.
From the first equality, we get a = d. From the second equality we get d = 2b. Three equations, four variables.

>N[{0.123, 1/3, 1, 2, 3}, 16]
>{0.123, 0.3333333333333333, 1.000000000000000, 2.000000000000000, 3.000000000000000}

how do i trim trailing zeros so it becomes
>{0.123, 0.3333333333333333, 1., 2., 3.}

>>9160605
also i wouldn't mind trimming leading zeros if it's not too complicated
>{.123, .3333333333333333, 1., 2., 3.}

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This question is in my textbook for the course and the answer given in the book is log(x)+C = arctan(y/x)-(1/2)log(1+(y/x)^2), but the course website for assignments says this is wrong.
So is the book or the site wrong?

>>9160613
truncation function/method in literally any programing language you nigger

>>9160099
Try multiplying both sides by
[math]\frac{\sqrt{1 - 2h - 2a}+\sqrt{1 - 2a}}{\sqrt{1 - 2h - 2a}+\sqrt{1 - 2a}}[/math]

>>9160618
how do i do it in mathematica

>>9160576
So there's no real term for it?

>>9160628
https://mathematica.stackexchange.com/questions/3736/annoying-display-truncation-of-numerical-results

>>9160629
they're just constants bruh, stop getting caught up over it

>>9160638
NumberForm[#, 16] &@{0.123, 1/3, 1, 2, 3}
>{0.123,1/3,1,2,3}

i need the 0.3333333333333333 i can't print the entire expressions

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How would I go about figuring out this problem?

>>9160647
holy shit i figured it out

test[x_, precision_] := ToString[N[x, precision], InputForm, NumberMarks -> False] &@x
test[{0.123, 1/3, 1, 2, 3}, 16]
>{0.123, 0.33333333333333333, 1., 2., 3.}

>>9160711
>&@x
it still works if you remove this since it doesn't use the # thing

[math] y = x^a [/math]
I know I can get a by calculating
[math] a = log(y) / log(x) [/math]
But how do i find a here:
[math] y = c \cdot x^a [/math]
where c is a constant?

>>9160773
just use the fact that log(ab)=log(a)+log(b)

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How do I go about finding an equation that represents t in terms of x?

Don't give me the solution, just looking for someone to point in the right direction here to solve this problem.

>>9157815
They were different races, not species. What we know today as races differs from the actual scientific term for race. This was done in order to justify enslavement (I believe it was the Africans being shiped to America via the Atlantic Slave Trade).

anyone have a book rec for physics tailored for computer scientists, and for quantum computing (regarding algorithms)? separate or in one book. i never took a single physics class in college (or highschool) so i'd like to round that out

Do I join a frat?

>>9156913
Hoe does the whole satellite system works, explain me from my mobile phone perspective.

i mean my phone send signal to the mobile tower and that tower is connected to satellite , so does that mean that the satellite sending information/signal to all the towers simultaneously.

IN OTHER WORDS

Does satellite send different signals to different receivers simultaneously at on time?
Cuz I always thought that if point A and B both comes under satellite coverage than the satellite send same information at both of the point and the receiver picks up whatever supposed to be "it's information" .
and if i am right than how the fuck a satellite transmit so much information? can i get the numbers? like how many bits per second or something like that.

>>9161095
no. they take your money and give other people alcohol. make irl friends

>>9161116
*How

how do i get a girl with math?

>>9161128
use math to make money

I'm having trouble understanding how to visualize a plane in [math]\mathbb{R}^{3}[/math] with just an equation like [math]3x - 2y + 3z - 4 = 0[/math]. Could anyone help me get a better understanding of this?

>>9161150
picture a plane perpendicular to the vector (3,-2,3) and containing the point (0,-2,0)

>>9161118
It's not just about friends though, they showed me powerpoints telling me how Mark Cuban and Mark Cuckerburg were in frats.
Will I become a millionaire if I join one?

>>9161150
Isolate z, watch for the coefficients of x and y and see how inclinated they are. Look for points (lines) where it intersects the axis. Alternatively, fuck visualization. Focus on the algebra and the methods, it's just as valid.

>>9161161
If you're not a very sociable person, don't do it anon

>>9161161
joining a frat's a great way to knock a few points off your GPA

What are the chances that I could do research with a professor at an undergraduate at a run-of-the-mill state school?

>>9161165
So you don't think it could mold me into a sociable person?

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WTF is a time crystal? And how do they work?

>>9161185
https://en.wikipedia.org/wiki/Quartz_clock

>>9161185
It's a type of crystal that has a regular repeating pattern that periodic in nature.

>>9161185
"crystal" was a misnomer. the end.

>>9160402
>Consider two real numbers
So-called "real" numbers can't really be shown to exist.

>>9160423
>Case 1
>Case 2
Prove that there are indeed two cases.

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Are these two groups of statements not the same?

In other words, the answer for question 1, would be this:

Statement 1: p ⇒ q
Statement 2: ¬p ∨ q

Wouldn't question 2 have the same answer?
I already did the truth table, I'm just trying to tell if the professor is throwing a curve ball.

>>9161381
"he must be" is a modal statement. They are not equivalent.

>>9161387
The bastard hasn't taught us that yet. I'm aware of the nuance from studying grammar, but I don't recall learning a symbol to represent that.

>>9161387
You know, searching "modal" and "must" in the pdf textbook isn't netting any results. I'm guessing if modal statements do exist in formal logic, he isn't bothering with it.

>>9161232
is crystallized intelligence a meme?

>>9155819

Thanks mate, it's appreciated.

glad to see I got it right.

>>9158622
It doesn;t really work they way you think it does. Growth if often triggered, controlled, or stopped by signals or things around it. Eg, if you had a small skull, your brain would still stop growing at a certain point to fit inside because its programmed to stop growing when it touches the skull(it doesn't actually touch your skull but you get my point).

In The Old Man and the Sea, I remember Santiago telling himself something like "The moon affects the ocean like it affects a woman"

I realized he meant women's mood when their period comes, since the cycle of the moon and "that time of the month" are on the same interval, is there any evidence that the two are correlated?

>>9161778
What do you mean by "periods"?

>>9160887
You mean x in terms of t? You could use something like Cardano's method to find the roots but that wouldn't be very practical. The better method is to find f'(5), g'(5) (using the implicit function theorem) and then use the product rule to compute h'(5).

>>9159818
In front of [math]y''[/math] you have only 1, so [math]\alpha(x) = 1[/math]
The homogeneous solution is [math]y_H(x) =
c_1+c_2x[/math]
So we have [math]y_1 = 1, y_2 = x[/math]
The Green's function is then
[math]G(x;\xi) = c_1+c_2x \quad\textrm{for} \quad x < \xi[/math]
[math]G(x;\xi) = d_1+d_2x \quad\textrm{for} \quad x > \xi[/math]
Continuity gives [math]c\xi = d(\xi-1) \rightarrow d = c\frac{\xi}{\xi-1}[/math]
The jump condition gives
[math]\frac{d}{dx}c\frac{\xi}{\xi-1}(x-1) -\frac{d}{dx}cx = \frac{1}{\alpha(x)} = 1 [/math]
The two derivatives are evaluated at [math]x=\xi[/math]

We get
[math]c\frac{\xi}{\xi-1}-c = 1 \rightarrow c = \xi-1 [/math]

Thus the Green's function is
[math]G(x;\xi) = (\xi-1)x \quad\textrm{for} \quad x < \xi[/math]
[math]G(x;\xi) = \xi(x-1) \quad\textrm{for} \quad x > \xi[/math]

To get the the solution y(x)

[math] y(x) = \int_0^1 G(x;\xi)f(\xi) d\xi = (x-1) \int_0^x \xi e^{\xi} d\xi + x\int_x^1(\xi-1)e^\xi d\xi [/math]

The integrals are easy, just integrate by parts and you get
[math] y(x) = e^x-ex+x-1 [/math]
The solution satisfies the initial conditions.

>>9159818
>like
No need to lie here, anon.

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Can someone please explain isomorphisms in graphs to me

I understand you can represent the same graph visually in multiple ways, pic related.

Am I correct in saying this is the same graph in my upload?

As far as i understand then an isomorphic graph to the one depicted is the same as depicted except the vertices aren't connected by the same edges. Is this understanding sound?

Is that to say to consider two graphs isomorphic, for every vertex in a graph there must be a corresponding vertex with the same degree in the second graph, even if labelled differently?

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I know the taught way (by using the quadratic formula) to derive arccosh(x), but what am I doing wrong here? Why isn't this working?

Whats a good book on the peano axiioms and arithmetic.

>>9162127
Try turning the picture around brainlet

how can I kill everyone on 4chan?

>>9162266
>how can I kill everyone on 4chan?
death would be too merciful for channers

>Let [math]n[/math] be an integer. Prove that [math]n[/math] is odd if and only if [math]n^{2}[/math] is odd.
[eqn]\left(\implies\right)[/eqn]
[math]n[/math] is a multiple of 3 and thus can be expressed as [math]n=3a[/math] for integers [math]a[/math]. So [math]n^{2} = 9a^{2} = 3(3a^{2})[/math] which is a multiple of 3 by definition
[eqn]\left(\impliedby\right)[/eqn]
Applying the contrapositive [math]n[/math] is not a multiple of 3 implies [math]n^{2}[/math] is not a multiple of 3. So [math]n \neq 3a [/math] thus [math]n^{2} \neq 3(3a^{2})[/math]. So by contrapositive, [math]n^{2}[/math] is odd implies [math]n[/math] is odd holds true

[math]\therefore[/math] [math]n[/math] is odd [math]\iff[/math] [math]n^{2}[/math] is odd , is proven true.

Is there a flaw in this proof? The [math]\impliedby[/math] direction seems too naive.

>>9162273
Why does n have to be multiple of 3 for it to be odd?

>>9162278
OH FUCK

Typed the wrong statement in. Should read, Let n be an integer, prove that n is a multiple of 3 if and only if n^2 is a multiple of 3

Is programming useful for a chemical engineer?

>>9162279
Right. n != 3a implies that n^2 != 9a^2 but that doesn't rule out n^2 = 3b for some other number b.

>>9162287
so should I then use another variable for the reverse direction to avoid confusion, or is this a more subtle issue?

>>9162289
It's not a matter of avoiding confusion. What you showed is that n^2 cannot have a specific 'form' which happens to be a multiple of 3. This doesn't prevent n^2 from having other forms which could be multiples of 3. I suggest working in modulo 3.

>>9162296
I see. Out of curiosity would the proof be possible without the use of modulo operator?

>>9162298
You could also use the fundamental theorem of arithmetic. Or you could just not mention the modulo explicitly. Something like n != 3a implies n = 3k + r where r = either 1 or 2, so square this expression and prove that the square would have a remainder of 1 or 2 when divided by 3 as well.

What book covers the peano axioms and arithmetic?

>>9162304
I understand how you write n=3k+r however how would I prove the square of this has a remainder of 1 or 2 when divided by 3?

Can someone solve this?
Prove that if [math]p-q, p^2 - q^2, p^3 - q^3[/math] are all integers then [math] pq(p-q) [/math] is also an integer.

>>9162317
n^2 = (3k + r)^2 = 9k^2 + 6kr + r^2 = 3b + r^2. 3b is obviously divisible by 3 but r^2 can only be 1 or 4 and both of these have a remainder of 1 when divided by 3, so n^2 also has the remainder as 1.

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>>9162326
ah, I see now. Thankyou.

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>>9162127
>>9162259

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What is the name of that shape?

>>9162318
[eqn]pq(p-q) = \dfrac{(p^2-q^2)^2 - (p-q)(p^3-q^3)}{p-q}[/eqn] Since p-q divides [math](p^2-q^2)^2 - (p-q)(p^3-q^3)[/math], the fraction is actually an integer

>>9162479
Fuck, that's good. How did you come up with the idea of rewriting it like that?

>>9159539
Learn the concepts, not the algorithm. It's way faster and harder to do. Good luck.

>>9162487
well I knew I kinda had to exploit the fact that our three numbers are integers so I knew I probably had to express it as some rational combination of the three
Also I knew that they were all divisible by p-q so I divided everything by p-q and tried to express pq in terms of 1, p+q and p^2+pq+q^2 instead.
Turns out that pq = (p+q)^2 - (p^2+pq+q^2). Rewriting this identity in terms of our original quantities gives the result

Why would someone build a circuit with a 48v dc power supply and a 10k resistor before the circuit over straight going with a lower voltage power supply? Seems like a unecessary waste of energy on the resistor.

>>9162511
Nice, thank you.

How do I stop being a brainlet

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The following
[eqn] A = \frac{1}{\binom{N}{M}} \sum_{n=1}^{N+1-M} n \binom{N-n}{M-1} [/eqn]
is supposed to reduce down to
[eqn] A = \frac{N+1}{M+1} [/eqn]
any clues on how to get there?

>>9162564
read

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tfw brainlet

>>9162476
trash can

>>9162579
btw are there any visible anomalies on my sMRI scan?

>>9162575
Think.

Is it appropriate to include additional definitions to my proof if I have to use methods outside of what's covered in lecture?

>>9156913
According to Srednicki a Lagrangian of only one-handed spinor fields [math] \mathcal { L } = \partial ^ { \mu } \phi \partial _{ \mu } \phi [/math] has a Hamiltonian that is unbounded below. Why is this? At first I thought that it was a consequence of Ostrogradsky's theorem, but you have similar kinetic terms in scalar field theories that don't have similar problems. Anyone got an input?

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How do i know if a crit point is stable or not?
I literally just guessed. I know that, from top to down, the curves are unstable, semi-stable, and stable, but how do I know what the crit points are?

>WARNING: VERY STUPID QUESTION
I'm trying to get drunk for cheap and thought of huffing some ethyl rubbing alcohol they sell near my house. Does the acetone in it evaporate as easily as the ethanol? If not, is there any easy way to remove it?

>>9162714
>but how do I know what the crit points are?
The critical points are the points where [math] y' = 0 [/math]

>>9162725
I meant when the crit points are stable, unstable, or semi-stable.

>>9162729
ask your mom to sit on them. if they don't break under her weight, they're stable

Is Operational Research worth taking as a module? I don't plan on becoming a suit's personal calculator. Does it have any interesting applications?

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>>9162393
Almost there though. If you ignored the first mistake and corrected the second, you'd get the square root part.

Differential Equations has been very difficult for me so far. Can someone recommend me an online resource with brainlet-tier explanations of diffeq concepts?

is there any way to improve working memory?

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Okay, this is starting to annoy me.

I'm not sure what I did here. This is from some homework I did a couple weeks ago. I'm going back through studying it. As you can see I found the answer, but I cannot recall how I got it.

When taking the limit from the left, the numerator becomes 3 -(-x), which is great because it comes to 3 + x like in the denominator and is an even 1.

But when I try to do it from the right, I hit a wall. It becomes (3-x)/(3+x)

I feel like the answer is ridiculously simple. I've been studying more or less all day, so my brain is a bit fried at the moment.

im fucking floored by this and i feel incredibly stupid:
prove
[math] \mid \frac{z}{\mid{z}\mid} - 1 \mid \ \leq \ \mid{arg \ z } \ \mid[/math]
ive tried reformulating it with definition of radian measure, using trig identities, definition of modulus of z, and i dunno what to try next. help

>>9162980
>But when I try to do it from the right, I hit a wall. It becomes (3-x)/(3+x)
this part is wrong, fix it then try again

>>9162968
sport improves insulation between neurons = better signal quality for a short duration.

Another big factor is encoding
130389789 is hard
130 389 789 is easier as you internally reduce 9 elements to 3.

There is also a big factor boosting recolection by 30% but sadly i forgot the details. Was something about how much you should take in before taking a break and internalize it first before learning the next chunk.

>>9162991
How is it not that? from the right the value of x isn't altered. So if it's 3-|x| shouldn't it become 3-x from the right?

>>9163002
> from the right the value of x isn't altered.
Why?

>>9163005
It's " X if X >= a
" -X if X < a
isn't it?

>>9163011
no
https://en.wikipedia.org/wiki/Absolute_value

>>9163013
So x is always going to be -(X) since -3 is less than 0? Is that the part I'm missing?

Need to do a question using both sides of the divergence theorem in spherical coordinates. But having trouble with the
[eqn]\iint _S\mathbf{D}\cdot \mathrm{d}\textbf{S}[/eqn]
part. I may have missed something obvious but what the hell is [math]\mathrm{d}\textbf{S}[/math]?

>>9163085
A small vector pointing outward of your sphere whose length is a surface element.

>>9161981
Anyone?

>>9163088
Engineer plz.

>>9161981
>>9163091

A good illustration for isomorph is imagine the edges between points are fixed but you can move the points arround. A is isomorph if you can move the points into a position that it becomes identical to graph B. ( your example fits isomorphism)

>>9162980
Seriously, I'm lost here.

Since |x| would be x if x >= 0
-x if x < 0
I can manage getting the -3 from the left, since the negative x and negative in the numerator cancel out to make a positive and give 1. But when I take the -3 from the right I get 3-x over 3 + x.

There are no other problems like this in my homework and only one other problem like it in the textbook, but of course it's one of them they don't give the answer to since it's not odd-numbered.

I'm used to dealing with limits featuring at least two things in them; those I can do easily.

>>9163094
I had to explain it in terms a physicist could understand. Pardon me.

>>9163147
>But when I take the -3 from the right I get 3-x over 3 + x.
no you don't

>>9163153
Then what am I supposed to get when doing it from the right?

>>9163134
Cheers.

So another example, these graphs are isomorphic it would seem to me.

What does mapping the vertex and edge set mean? In terms of V(G) -> V(G'') and E(G) -> E(G'')?

Surely it doesn't mean just writing both sets in the order that each edge and vertex match each other? I thought sets were unordered.

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>>9163326
Pic related, sorry

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>>9163326
Shit, the figure associated with these problems in my text was in a different chapter.

Pic related, this is this the form my answer should take I believe. Obviously this is for a different example.

I was never taught basic math and at this point I'm to afraid to ask.
(I can add and subtract and other stuff like that but I can't do even very basic algebra. Think that I have an 8th grade education in math)
What do I do /sci/?

>>9163354
Start

>>9163379
Could you elaborate a little please?

>>9163387
Find out where a 9th grade education in math begins and start learning.

You have access to all human knowledge, you might as well utilize it.

>>9162695
2hard4u?

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How do I write something like pic related in LaTeX?

>>9163561
Use cases. [eqn] G (x,t) =\begin {cases} h_1 (t) y_1 (x), ~ x< t \\ h_2 (t)y_2(x), ~ x> t \end {cases} [/eqn]

>>9163565
Thank you

>>9163566
np.

>>9162966
Anyone?

>>9163734
Pauls online math notes
http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

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[math]0 \longrightarrow M \overset{\varphi}\longrightarrow N \longrightarrow \mathrm{coker} \, \varphi \longrightarrow 0[/math]
I have this short exact sequence of modules and I'm reading a proof of the sequence being split iff [math]\varphi[/math] has a left inverse.
I might be retarded, but can someone explain how [math]\mathrm{ker} ~\psi[/math] got involved here? Is it isomorphic to [math]\mathrm{coker} ~ \varphi[/math]?

Trying to prove [math]5^{n} + 9 < 6^{n}[/math] by mathematical induciton.

Base case here is n=2
[eqn]5^{2}+9<6^{2} \implies 34 < 36 [/eqn]
Now for the inductive step, assuming [math]k[/math] holds with
[eqn]5^{k} + 9 < 6^{k}[/eqn]
then [math]k+1[/math] will hold
[eqn]5^{k+1} + 9 < 6^{k+1}[/eqn]
Manipulating the hypothesis:
Manipulating the hypothesis:
[eqn]\left( 5^{k} + 9 < 6^{k}\right) \cdot 6 \implies \left( 6\right)\left(5^{k} + 9 \right)< 6^{k+1} \implies (5+1)\left(5^{k} + 9 \right)< 6^{k+1}[/eqn]
[eqn](5+1)\left(5^{k} + 9 \right)< 6^{k+1} \implies 5^{k+1}+9 +5^{k}+45 < 6^{k+1}[/eqn]

Now, call me a brainlet, but I don't understand this next step. Apparently we can 'disregard' the [math]5^{k}+45 part of the inequality since we know that [math]5^{k+1}+9 < 6^{k+1}[/math] and that [math]5^{k}+45 > 0[/math]. Why can we do this? Is is transitivity of inequality or something?

>>9163739
Thanks m8, looks like a good resource.

>>9163764
seems like you don't need to multiply out since 5+1 is 6 and 6^k+1 is 6*6^k and then you can use the hypothesis

>>9163764
or, I guess to simplify my question

why can we write [math]6^{k+1} > 5^{k+1}+9 + 5^{k}+45[/math] as just [math]6^{k+1} > 5^{k+1}+9 [/math]

>>9163769
is it something along the lines of if [math]a>b[/math] then [math]a>c_{1}+c_{2}+\dots c_{n}[/math] where [math]\sum_{i=1}^{n} c_{i} = b[/math]

>>9163768
sorry, I don't quite follow

>>9163768
since 5^k+1+9<5^k+1+9+5^k+45<6^k+1 the hypothesis holds

>>9163779
ahhh, that makes sense.

>>9156928
http://www.askamathematician.com/2011/03/q-why-does-emc2/

I'm just starting with LaTeX, at the moment every line of equations gets a number, how do I make it so that only the ones I want are numbered?

>>9163764
Whats happening is that they're saying is that since [math] k > 2 [/math] then [math] 5^{k+1} > 0 [/math] and so [math] 5^{k+1} + 9 + 5^k + 45 > 5^{k+1}+9 [/math] so then we can say that [math] 5^{k+1} < 5^{k+1} + 9 + 5^k + 45 < 6^{k+1} [/math], it's not so much ignored, more just omitted. You could still include it if you wanted.

>>9163789
you could put equations in their own block of $$ $$ and the ones you want numbered in \begin{equation} for a simple soultion. I think there's an argument you can feed into \begin{equation} that does it too, would have to look at the documentation.

>>9163791
Many thanks.

>>9163789
For inline math you can use $ $, for centered math you can use \[ \]. The latter reproduces \begin{equation} without the number.

>>9163794
>>9163800
I found out you could write

\begin{align*}
no number
\end{align*}

Also, I use align for everything I want centered, what's the difference to equation?

>>9163812
https://www.sharelatex.com/learn/Aligning_equations_with_amsmath
it can align equations for you

>>9157098
It didn't happen at once, evolution takes many many generations, those with just a little less fur had a slightly better chance to survive so their genes got passed on.

>>9163326
you just write it down ordered to make it easier to visually compare the sets. If one graph has more points they can't be equal, same if one has 5 edges for a point while the other largest is 4. If the vertex and edge sets are equal however you can easily map them to each other.

What is [math]\mathbb{R}\setminus \mathbb{Q}[/math] ?

>>9163872
The empty set

>>9162987
anyone able to help

>>9163872
>[math]\mathbb{R}[/math]
That's a weird symbol to use for [math]\mathbb{Q}[/math].

>>9163900
What is the empty set?

Is it true that an itegral is defined as the area under a function from x=0 until the specific x Value?
Then why do the integrals of some fuctions evaluate to 1 at x=0? for example e^x
At x= 0 it has the value 1, which would mean that the area under its derivative would be 1, which doesnt make sense, because the base (change in x) is 0.

>>9163993
Integrals can be used to calculate the area under a graph from a point a to another point b. This only applies to definite integrals though.

Indefinite integrals can be thought of as the inverse of a derivative.

As [math]\frac{d}{dx}e^x = e^x[/math] you also get [math]\int e^x dx = e^x +c[/math] where c is some arbitrary constant.

>>9163993
> Is it true that an itegral is defined as the area under a function from x=0 until the specific x Value?
No.

A definite integral is defined over a given range. An indefinite integral (antiderivative) has a constant of integration which reflects the fact that the lower bound is unspecified.

>>9163993
>>9164034
If you want to evaluate a definite integral of say [math]e^x[/math] you get

[math]\int_a^b e^x dx = [e^x]_a^b=e^b-e^a[/math]

>>9157198
You are wrong the total energy of a system is its mass + energy

https://plato.stanford.edu/entries/equivME/

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It's probably really easy but can someone explain this to me? The union and intersection notation of a single set is unclear for me.

>>9164050
For each m/n you have an infinite intersection/union.
Intersection of A_{m,n} = {k in N : mk < n for all m}
for a set n, for how many k is mk < n for all m?
Now take the union,
Union A_{m,n} = {k in N : mk < n for any n}
for a set m, for how many k is mk < n for some n?

>>9164038
>>9164037
>>9164034
thanks for the responses.
So i just understood why c is the lower bound.
But is there an intuitional explanation what the indefinite integral is? The area under a curve, from some point(which point?) to x?
Its definitely a sum of infinitesimally small changes in x times the value of the function at that moment. But from where to where does it get added up, if not from zero to x?

>>9163764
5^{k+1}+9=6*(5^k+9)-5^k-45<6^{k+1}-5^k-45<6^{k+1}

>>9164101
The indefinite integral is just the inverse of the derivative.

>>9164121
Yes i know, but it also happens to be an area, but what area? Or maybe there is just no way to picture the indefinite integral and the area under a curve property only applies to definite integrals?

>>9164126
>the area under a curve property only applies to definite integrals?

Yes.

>>9164127
Ok, so that was the mistake. Thanks alot, anon.
But can you explain why the definite integral over an interval from a to b is the indefinite integral evaluated at b minus the indefinite integral evaluated at a? F(b)-F(a)

Am I allowed to use gauss elimination on this equation system:
a^2-b^2 = -11/4
ab=-15i/2
Because I suspect that doing that is what's causing me get a completely absurd result later on in the exercise (that the real coeffecient of a complex expression would be complex).

>>9164134
indefinite integral evaluated at x is the definite integral from minus infinity to x

>>9164145
Ok now everything makes totally sense, thanks a lot!

anyone here know shit about gel electrophoresis?

Why does the Benedict's test need a hot water bath? What does the heat do?

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How do I solve this?

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I don't know where to begin in order to prove that [math](C^1([0, 1]), ||f|| + ||f'||)[/math] is a Banach-space, where [math]C^1([0, 1])[/math] is the set of all continuously differentiable functions [math]f:[0, 1] \rightarrow \mathbb{R}[/math] and [math]||f|| = max_{x\in [0, 1]}|f(x)|[/math].

I know that for it to be a Banach space, all Cauchy-sequences in said vector-space must converge in [math]C^1([0,1])[/math]. So I attempt proof by contradiction by picking an arbitrary Cauchy-sequence and assuming it doesn't converge. But I have not the slightest clue on how to arrive at a contradiction here.

Is there some general approach to these kind of problems? I guess I am asking for a push in the right direction or a way of thought which could get me going in the right direction by myself.

pic related, book I'm using

>>9164145
> indefinite integral evaluated at x is the definite integral from minus infinity to x
The indefinite integral evaluated at x is the definite integral from some arbitrary point to x. This is why the indefinite integral always has an arbitrary constant of integration, c.

E.g. the indefinite integral of f(x)=x is F(x)=x^2/2+c. If you differentiate F(x), the constant c disappears. Similarly, if you calculate the definite integral F(b)-F(a), the c's cancel and disappear.

>>9164126
> the area under a curve property only applies to definite integrals?
For the area of a region to be something other than infinity, the region needs to be bounded. For a definite integral F(b)-F(a), the region is bounded by x=a and x=b, as well as by the curve y=f(x) and by y=0.

Also note that for any k, F(x)-F(a) = F(x)-F(b) + (F(b)-F(a)) => (F(x)-F(a))-(F(x)-F(b)) = F(b)-F(a). IOW, changing the lower bound simply shifts the integral by a constant.

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How do I solve for c?
When I integrate, I get:
arctanx = 4t+c

I don't understand how my book found C when t isn't given.
Their answer for C was -3pi/4

>>9164560
>How do I solve for c?
try using the only information given in the question you haven't used yet

>>9164563
I'm dumb. What should I do? I plugged in pi/4 in arctanx and t and I still don't know how they came up with that solution.

>>9164582
You just plug in pi/4 and rearrange for c, I don't see where you could get stuck

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why are they not equal what the FUCK

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if i wrap everything in parens it simplifies to {0,0} but can you explain what they mean in pic related?

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>>9164645
but those results ARE equal

>>9164661
mathematica is being dumb tho >>9164653

>>9164609
Plug in pi/4 for t for 4t+c=1?
When I do that, I get c=pi, but the answer is supposed to be -3pi/4

>>9164671
>Plug in pi/4 for t for 4t+c=1?
Where did 4t+c=1 come from?

>>9164679
When i integrated, i got arctanx = 4t + c

>>9164693
>When i integrated, i got arctanx = 4t + c
Ok? Where did 4t+c=1 come from?

>>9160500
Doesn't g(x) not exist at that point?

>>9164693
and x(pi/4) = 1

>>9164696
i set it equal to one because if i plug in pi/4 it should be equal to one

>>9164706
>i set it equal to one because if i plug in pi/4 it should be equal to one
Why?

>>9164709
x(pi/4) = 1

>>9164720
Yes, plug that into your solution for the differential equation

>>9164720
x and arctan(x) are different numbers you gigantic retard