Hello everyone! I've recently decided to improve my calculus abilities by going through the book "Advanced Integration Techniques" by Zaid Alyafeai. I am trying to derive the Beta function using a Laplace transform. I have essentially started by defining two functions, f(t) = t^x and g(t) = t^y, then I take the Laplace transform of their convolution. This yielded the function F(s) = x!y!/s^(x+y+2). However, I'm having a lot of trouble converting back from the s to the t domain. This may just be a super stupid oversight on my part, but I've been staring at the Inverse Laplace table, and I haven't really been able to make any progress. Any help would be greatly appreciated.

Btw, I remember reading somewhere that this subreddit accepts latex equations, so I wrote it in that format. However, if that particular piece of information came to me in a delusion, I apologize.

Edit: Turns out, the latex didn't work, so I made it less confusing. hopefully.

https://i.redd.it/akxpy9gww05e1.jpeg

This photo has sparked a war in my friend group. Specifically Mark (26M) refuses to accept that the answer is anything other than 36, because as he says, “it says 36 right there.” I’m curious how you all would go about breaking this down in the simplest possible way for people who just can’t understand. (We got this from Reddit because the OOP was commenting on how it’s written wrong and the only correct answer involves half dogs!)

Edit to add: to clarify, Mark isn’t saying there are any dogs besides small and large. He is confident there are 36 small dogs and 13 large dogs.

hey guys

so there is this type of questions I am always having a bit of difficukt time with.

for example this is one question I was given:

let A, B, C be sqare matrices. its known that C(I+AB)=I and BA=B.

prove that (I-BC)(I+B)=I

i understand the concept of the question but my methods are not evolved enough to solve this types of questions fluidly.

if you have tips or resorces I would appreciate it alot.

thank you.

I know what they are and how to use them, i just don't understand the difference between "n pick r" and "n choose r"

Hi,

I'm a student in a video game course and the more I learn, the more I realize that if I want to be proficient in it and understand everything, I really need to get better at maths... But I'm really bad at maths, never learned a lot at school and is definitely in need of help to understand anything maths related.

I've seen people recommending Khan Academy, and I'll definitely make an account to learn the basics but after it, I don't really know where to focus my energy. Maths is really vast and I'm not sure which part of it I need to focus to stay in course with my studies. I want to focus in the tech art domain, but I don't know what this encompasses exactly.

I guess anything link to programming, and computer graphics? Maybe some geometry, I've heard that trigonometry is really important?

So yeah, if there's anybody that knows what are the specific domains I need to work on and where to begin in those (or resources about them), it would be awesome, I'm really at a loss and have no idea where to begin

Thanks and have a nice day!

I really wanna relearn math because I want to see the world differently. However, I did, unfortunately, study at kumon, and I am very averted to puzzles and all the like. Do you have anyway to undone those damages?

I've had this series bothering me for the past week,<br>

$sum_{n=0}^{+\infty} \frac{1}{(n^2+1)^2} * log_2(\frac{1}{(n^2+1)^2)$ <br>

it should converge to

$\frac{1}{96} Log_2 (48 + 15 \pi Coth[\pi] + 15 \pi^2 Csch[\pi]^2 + 12 \pi^3 Coth[\pi] Csch[\pi]^2 + 4 \pi^4 Csch[\pi]^4 + 2 \pi^4 Cosh[2 \pi] Csch[\pi]^4)$

but i can't prove it analitically for the love of me.

ie, proving that for all a>0, a^(b)=a^(c) iff b=c, and I don't think we can use logs here as if exponentials weren't one-one in the first place, logarithms would've not existed, this also includes proving that a^(b)=1 only when b=0

edit: thanks everyone!!

“dh/dt = - sqrt(5h) Determine d^2h/dt^2 at h = 16”

The answer key says it equals -5/(2*(5h)^1/2) * dh/dt, which makes total sense except for the last part. Why do we have to implicitly differentiate here whereas in a generic physics problem such as “Find the instantaneous rate of velocity” and given the equation x = 3x + 4, it equals v = 3 rather than v = 3* dx/dt? this disagreement in my calculus used for calc class and calculus used for physics class makes no sense, please help…

I asked lots of people from Reddit about how much they could solve from imo Olympiad without time limit vs in time limit of Olympiad 9h. 16 people answered on that. Which means that they tried both variants timed and untimed.

Before understanding results you should know that level of difficulty is different from different years of imo. 4 items from 2017 is as difficult as all 6 items from 2005 year. You can see that in statistics on website. Average speed on timed usually looked like 2.5 if someone can solve 2-3 on timed case. 15 of those 16 could solve at least 2 items in complex year. Or 3 in simple year.

I found that more someone can solve untimed so more will be distance from his untimed score to his timed score. For example someone can do 3 timed and 4 untimed. Other can do 4 timed and 6 untimed. So that 6-4 > 4-3.

I was asking about actual results. So that means how much someone actually solved not how much he predicts that he can solve.

Untimed means without time limit.

So here are norms.

Av s = means average speed.

S u = means how much someone can solve in simple year as 2005. Untimed.

C u = means how much someone can solve in complex year as 2017. Untimed.

Av s 2.4 => s u 3.3. , c u 2.2

Av s 3.625 => s u 6. , c u 4

Av s 4.625. => s u 6 , c u 5.5

Which means that if someone solved all 6 items in 2005 or 4 items in 2017 I predict his average speed on timed Olympiad as 3.625

Also which means that if someone solved 3.3 items in 2005 or 2.2 items in 2017 I predict his average speed on timed Olympiad as 2.4

I'm playing a tile based game. And Here and there I know that to keep my layout, I have to put a street in a certain angle.

Example:

I want three streets from the middle into all directions. Obviously there's a 120° angle between all of them. The top street just goes up.

So I know that I need an angle of 30° downwards from the x axys to the left and right to keep it even.

How do I find the linear function for this?

I need something that tells me to put three street tiles right and then one step down and three tiles right again, etc.

Obviously I won't get round numbers, but y=1 and x=2,5 let's me translate it to alternating 3 tiles and 2 tiles while going one step down.

I don't understand the steps, but the answer is:

D(g)={x∈R| x≠5π/12 + (kπ/2) k∈Z}

My proof goes as follows:

n=/ (doesn't equal) c^2 where c is a member of the set of all natural numbers (N).

sqrt(n) = a/b where a and b are coprime and are both in the set N.

n=a^2/b^2 =>

n*b^2=a^2

If a^2 is a multiple of n, a is a multiple of n.

The proof of the statement above goes as follows:

Proof by contradiction: Assume that if a^2 is divisible by n, a isn't divisible by n.

then a = n*k + m, where k is in the set N and m is in the set: {0,1,2, ..., n-1} which is a subset of the set N. => m is not divisible by n.

Then (a^2)=(nk+m)^2 =>

a^2 = n^2k^2+2nkm+m^2 =>

a^2= n( n*k^2 + 2km) + m^2

Since m=/ n*j where j is in the set N, m ≡/(not congruent to) 0 (mod n) =>

m^2=m*m≡/0 (mod n) <multiplicative property of modulus>

The statement above is only true if m=/ sqrt(k)* sqrt(n), and since for the sqrt(n) to be a natural number, n must be a perfect square, a contradiction of the initial conditions, m^2≡/ 0 (mod n) is true for all relevant numbers.

Thus since m^2 isn't divisible by n, there is a remainder R=m^2(mod n) such that a^2 =n(n*k^2+2km+o)+R.

Thus a^2 isn't divisible by n when a isn't divisible by n. This is a contradiction of the initial statement that a^2 is divisible by n.

Therefore, if a^2 is divisible by n, a is divisible by n.

Thus a^2 can be written as a^2 =(np)^2 where p is in the set N. =>

a^2=n^2p^2 =>

b^2=n*p^2

And since b^2 is divisible by n, b is also divisible by n. Since both a and b are divisible by n, a and b are not coprime. Therefore this results in a contradiction. Thus the sqrt(n) is always irrational if n is in the set N but not a perfect square. Q.E.D.

there's this example dealing with product of 2 Laurent series of with pole of order 2 , and they argue the calculation legal due to absolute convergence, and i have no clue how is this happen or seen

in general we have f=sum from -inf to in a_n*z^n , and we problem about finding Res_0 for f^2, now f^2 is cauchy product , i know that Laurent series converge in annule , but just convergence isn't enough, we need it to be absolute convergence if I'm not mistaken t=so that the product also convergence .

so that's my problem i dont understand why it was argued by abs conv. i dont even see why it's abs conv

Hi friends of reddit. First off, apologies if I'm writing in the wrong subreddit. I'm trying to learn how to solve a problem I have and I am hoping I'm asking the right crowd here.

I'm dealing with some procedural computer graphics and essentially what i'm trying to do is turn a sharp corner into a smooth one (still with discrete points mind you, only more than one).

Please see this image: https://imgur.com/a/I93swqJ

I'm trying to get from knowing p0, p1, and p2, to a smooth corner by calculating p0', p1', p2', p3', and p4'. Ideally the number of vertices on the smooth corner is arbitrary so I can adjust it.

From a quick search I see suggestions of fitting a spline or running a gaussian kernel to smooth the values, but I'm curious if there's any specific option suited for this.

Thank you!

Edit: thank you all for your suggestions, it was nice to dive into different options. Evaluating a bezier like u/Chrispykins suggested was the simplest solution for my case.

Can someone please integrate sinxcosx using the DI shortcut please? I am getting sin^2x-cosxsinx+C and I have no idea where I am messing up

D

sinx

-cosx

+ -sinx

- -cosx

I

cosx

sinx

-cosx

-sinx

But you would stop at the second row as it is repeated, making the answer

sin^2x-cosxsinx+C

I have been given a question which states that:

GCD(a,m) = d & GCD(b,m) = 1

I must prove that GCD(ab,m) = d.

Now i think i know that GCD(ab,m) = GCD(a,m) * GCD(b,m), but I was wondering how the distributive law here works to give us GCD(ab,m), and if it doesn't, what is a proof that does work.

I have 6 days to study for a Linear Algebra with A_pplications Final Exam. It is cumulative. There is 6 chapters. Chapter 1(1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7), Chapter 2(2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9), Chapter 3(3.1, 3.2, 3.3, 3.4), Chapter 4(4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9), Chapter 5(5.3), Chapter 7(7.1, 7.2, 7.3). The Unit 1 Exam covered (1.1-1.7) and I got a 81% on it. The unit 2 exam covered (2.1-2.9) and I got a 41.48% on it. The unit 3 exam covered (3.1-3.4, 5.3, 4.1-4.9) and I got a 68.25% on the exam. How should I study for this final in 6 days to achieve at least a 60 on the final cumulative exam?

We were using Williams, Linear Algebra with A_pplications (9th Edition) if anyone is familiar

Super wordy but I been thinking about it a lot as this is the semester I graduate if I pass this exam

Hi. I'm looking for a Calculus 3 (Multivariate Calc) asynchronous course. I cannot use any sort of third-party certifications; the credit needs to come directly from a somewhat accredited university. I also would not be able to take any in-person proctored exams, as I will be working full time during the course. Price isn't too much of an issue.

I've already looked at the University of ND's self-paced Calc 3 course, but I've seen some pretty worrying info about the prof, so this would be my potential last resort. I've also checked out a few community colleges but haven't had any luck.

I'm a student in Michigan if that makes a difference.

Thanks!

Me and some of my friends were arguing, and we couldn't find a decisive answer online. When rounding to the nearest whole number, how many numbers back do you go? For instance, would 3.499999 round to 4 because it rounds to 3.5 as the nearest tenths place, which rounds to 4 as its the nearest whole number to 3.5? Or, in this case, 6.849. Since a 6 is in the hundredths place, wouldn't it automatically disqualify the number from ever rounding above 6.8 when rounding to the tenths place.

Anyone have a recommendation for a good book just to practice problem solving? I want to take the IMC in summer so need to get cracked

What is the smallest group that, in order to be defined by extensions of simple groups, requires an extension that is not a direct product or a semi-direct product?

Hi everybody!!
Its my first semester on my double major (pure math + computer engineering) and I have my linear algebra (proof based) final in a week.

I don't have class anymore so I have around 5-6 full days just to study for this final, but the problem is I've been focusing on all of my other classes (as this one didnt seem as hard and I have 5 other classes I had to study for) so I almost know nothing and haven't even attended the lectures for the last topic (8) because I was too lost.

The topics for the final are going to be (I'm not doing my course in english so some words might be wrong):

1. Basic stuff with matrix: Operations, solving systems of equations with them, Gauss-Jordan, etc
2. Inverse matrix
3. Span, linear independence, etc
4. LU Factorization
5. Vector Spaces
6. Linear Transformations
7. Determinants
8. Eigenvectors and eigenvalues

(I probably missed some stuff because I don't know how to translate it but I'm working with Chapters 2,3,4, and 6 from Davide Poole's Introduction to Linear Algebra)

Exam is going to be 50% excercises and 50% proofs or theory-based exercises. I'm hoping I can read through the book and look at the examples and work with the excercises at least, and then try and learn and understand as much proofs and theory as possible.

Do u think its possible? (Topics 1 to 4 I understood them in class, except for the proofs which I didn't look at). And do u guys have any advice on how to learn this as quickly as possible or what to focus on?

Thanks for your time :)

First of all, I'm always really unsure whether what I have written is correct, so please could people check my part (a) and ==> direction for part (b)?

I have provided my thinking for part (b) <== direction, but I'm very stuck.

And I feel like I have the idea for part (c), but again I feel stuck so please does anybody have any hints?

Also does anyone know how to build "confidence" with proof based courses because whenever I write a proof I'm really unsure whether it is correct or not, compared to methods based courses.

Question: https://ibb.co/wLtR9CS

My attempts:

part (a) https://ibb.co/yy5n8mL

part (b) ==> https://ibb.co/XpQ2nVL

part (b) <== https://ibb.co/7Wk193B

part (c) https://ibb.co/Fb08Bk1

It's for an important project and I'm wanting to make sure I'm laying out the steps correctly for the teacher https://imgur.com/a/SmqkmKx Thanks!

5. A manufacturing firm orders computer chips from three different companies: 20% from Company A, 30% from Company B and 50% from Company C. Some computer chips will be defective: 5% of chips from Company A, 3% of chips from Company B and 0.5% from Company C.

a) A worker discovers that a specific chip is defective....What is the probability that the computer chip came from Company B? (Show your work)

I got 0.009

When finding the p-value using the t-table is it right to say that if the t test statistic is positive while the left tail is tested or the t test statistic is negative while the right tail is tested, we will subtract the found range (from the t-table ) of alphas from 1 to find p-value. But if the test statistic is negative while the left tail is tested or if the test statistic is positive while the right tail is tested, we will not subtract from 1, but take the range of alphas as given from the t-table as the p-value. And if it is two tails test, we will simply multiply the found range (from the t table) of alphas to 2, regardless of whether the test statistic is positive or negative

Consider the following game played between players 1 and 2. Player 1 moves first and plays either L or R. This is observed by both the players. If L is played, players 1 and 2 simultaneously choose from the sets {l, r} and {t, d} respectively and the game ends with payoffs (3,1), (0,0), (0,0) and (1,3) if (l,t), (l,d), (r,t) and (r,d) are played respectively. If Player 1 plays R, players 1 and 2 simultaneously choose from the sets {m, n} and {q, s} respectively and the game ends with payoffs (2,2), (0,0), (0,0) and (0,0) if (m,q), (m,s), (n,q) and (n,s) are played respectively.
1. Represent this game in extensive form (draw the game tree only).
2. Find all subgame perfect equilibria (SPE) of the game.

I've figured out that the L branch has two nash equilibrium's, both pure; and the R branch has one. I am not able to approach the second subpart beyond that. if someone could help me solve it that'd be great, tia!

i am doing calculus, but i found out there are many Algebric concepts (such as 1/1/x = x) which i didn't know, as also as slope equations. also in programming we are doing a lot of linear algebra.

is there a collective roadmap where i can learn these things for free?

I bombed my first Linear algebra test, got a 1/10 in a test worth 33% so now i'm looking to change how i study, does anyone know any good resources for linear algebra?

My class is more focuses on computing rather than theory or proof, and i'm struggling understanding what the question are asking of me and making stupid mistake while doing matrizes and linear system like mistaking number and simple math rules

The teacher will also allow me to retake the test at the end of the semester so i'm going to focus on studying everything from the start again.

I'm studying using a textbook from another teacher from my college, but i used my professor question sheet for the test, so i did around 16 matrixes question for this test, i did not do any of the textbook questions.

I'm confused since i was going really well this semester, even nearly getting a 10 in calc b,so any help would be nice.