SuicideFuel Math thread problem (official)

[Ahnfeltia]

yea at one point you just know the method but don't bother to compute the integral because we aren't first year math students lol.

I tend to do too much in my head. I could benefit from writing out more stuff. In this case however, I'm confident I could solve those integrals off the top of my head. Nice assortment of integrals btw.

 

[Ahnfeltia]

Start off by evaluating points D, M, M’, D’ of the elipse.

You can solve it with elementary math

I think that's exactly what I tried. If I'm not mistaken, the Cartesian coordinates (taking the center of the ellipse as the origin) of M & M' are pretty ugly (involving quadratic surds). Is that right?

 

[Fallenleaves]

Compute the integral of 1/(1+x^5)

ln|1+x^5|+ C

 

[Ahnfeltia]

Find the function f(x), such that

f((x-3)/(x + 1)) + f((x + 3)/(1 - x)) = x

Let g(x) = (x - 3)/(x + 1). Note that g(g(x)) = (x + 3)/(1 - x) and g(g(g(x))) = x. We are given that f(g(x)) + f(g(g(x))) = x. Ergo

• f(g(g(y)) + f(y) = g(y)
• f(z) + f(g(z)) = g(g(z))

where we plugged in x = g(y) and y = g(z). Subtracting the OG equation from the sum of the two derived equations yields that 2f(w) = g(w) + g(g(w)) - w. Simplifying results in f(x) = x(7 + x^2)/(2 - 2x^2).

 

[Ahnfeltia]

ln|1+x^5|+ C

False. If you differentiate this, you'll get a factor of 5x^4 because of the chain rule.

 

[Fallenleaves]

False. If you differentiate this, you'll get a factor of 5x^4 because of the chain rule.

It's impossible, IBP, trig sub, u-sub and IBPF can't be used

 

[Fallenleaves]

Why are there 20 bluepillers

 

[Fallenleaves]

-(Lim x--->0 (| 2x - 1| - | 2x + 1|)/x)

4

 

[trying to ascend]

4

Correct

 

[Ahnfeltia]

It's impossible, IBP, trig sub, u-sub and IBPF can't be used

You can totally use IBPF. After all, 1+x^5 has a zero at x = -1.

 

[Caesercel]

My nigga @Caesercel you answer basically everything.

Its just old practice. And I don't answer everything, only problems I can casually solve in my head. A few other users are pretty good

 

[Caesercel]

math PhD student

Number theory?

 

[trying to ascend]

It's impossible, IBP, trig sub, u-sub and IBPF can't be used

I mean, if you want to undo an implicit differentiation, all those may not work

 

[trying to ascend]

Be f(x) a cubic polynomial with real coefficients, such that:

∣ f(1) ∣ = ∣ f(2) ∣ = ∣ f(3) ∣ = ∣ f(5) ∣ = ∣ f(6)∣ = ∣ f(7) ∣ = 12.

Find ∣ f(0) ∣

 

[Marathon]

old practice

How Tf do you remember this shit? Brutal you could have saved from the test years ago where I was humiliated

 

[Ahnfeltia]

Number theory?

Nope. In the direction of probability, statistics and approximation theory.

 

[Ahnfeltia]

Be f(x) a cubic polynomial with real coefficients, such that:

∣ f(1) ∣ = ∣ f(2) ∣ = ∣ f(3) ∣ = ∣ f(5) ∣ = ∣ f(6)∣ = ∣ f(7) ∣ = 12.

Find ∣ f(0) ∣

Let p(x) = f(x - 4). Then |p(±1)| = |p(±2)| = |p(±3)| = 12. Supposing p is odd, we want to find a & c such that p(x) = ax^3 + cx and |p(1)| = |p(2)| = |p(3)| = 12. We can turn this into a linear system of equations -- namely

• a + c = p(1) = ±12
• 8a + 2c = p(2) = ±12
• 27a + 3c = p(3) = ±12

Because the above linear system is overdetermined, we should be able to express one of the three left-hand sides as a linear combination of the other two. Indeed, 4(8a + 2c) - 5(a + c) = 27a + 3c, so we immediately see that p(1) & p(2) must have the same sign. Which sign p(1) & p(2) share doesn't matter, because swapping the sign would amount to negating p and we're only interested in the absolute value of f(0) = p(-4). WLOG we'll therefore solve

• a + c = -12
• 8a + 2c = -12

Skipping the boring details, a = 2 & c = -14, so p(x) = 2x^3 - 14x and |p(-4)| = |2*64 - 56| = 72.

---

Anyone else care to prove that the p I've found is the only solution (up to sign) to the system |p(±1)| = |p(±2)| = |p(±3)| = 12?

 

[Fallenleaves]

@trying to ascend @Ahnfeltia

What exactly does convergent and divergent mean when calculating improper integrals, I get the definition but is there some meaning behind the 2 ways of describing improper integrals?

 

[Fallenleaves]

You can totally use IBPF. After all, 1+x^5 has a zero at x = -1.

Very funny

 

[Fallenleaves]

What area of math should I self-study after calculus? @Ahnfeltia @trying to ascend

 

[Fallenleaves]

Undefined

Infinity

 

[trying to ascend]

Infinity

No, because there is a discontinuity in infinity

 

[trying to ascend]

What area of math should I self-study after calculus? @Ahnfeltia @trying to ascend

Linear algebra

 

[trying to ascend]

Let p(x) = f(x - 4). Then |p(±1)| = |p(±2)| = |p(±3)| = 12. Supposing p is odd, we want to find a & c such that p(x) = ax^3 + cx and |p(1)| = |p(2)| = |p(3)| = 12. We can turn this into a linear system of equations -- namely

• a + c = p(1) = ±12
• 8a + 2c = p(2) = ±12
• 27a + 3c = p(3) = ±12

Because the above linear system is overdetermined, we should be able to express one of the three left-hand sides as a linear combination of the other two. Indeed, 4(8a + 2c) - 5(a + c) = 27a + 3c, so we immediately see that p(1) & p(2) must have the same sign. Which sign p(1) & p(2) share doesn't matter, because swapping the sign would amount to negating p and we're only interested in the absolute value of f(0) = p(-4). WLOG we'll therefore solve

• a + c = -12
• 8a + 2c = -12

Skipping the boring details, a = 2 & c = -14, so p(x) = 2x^3 - 14x and |p(-4)| = |2*64 - 56| = 72.

---

Anyone else care to prove that the p I've found is the only solution (up to sign) to the system |p(±1)| = |p(±2)| = |p(±3)| = 12?

Correct

 

[Ahnfeltia]

Very funny

that was not a joke

Wolfram Mathematica disagrees. Curiously the solution features the golden ratio prominently. I imagine the way to solve for the antiderivative of 1/(1+x^5) is to notice that 1+x^5 = (1+x)(1-x+x^2-x^3+x^4) and to further notice that 1-x+x^2-x^3+x^4 = (1+ax+x^2)(1+bx+x^2) for some a & b by the fundamental theorem of algebra and judicious guessing. Solving for a & b readily yields that -- without loss of generality -- a is minus the golden ratio and b is the reciprocal of the golden ratio. At this point, you can probably go thru some onerous partial fraction decomposition to arrive at the answer.

 

[Ahnfeltia]

What exactly does convergent and divergent mean when calculating improper integrals, I get the definition but is there some meaning behind the 2 ways of describing improper integrals?

Improper integrals are limits. Convergent improper integrals are limits that converge to an actual number. Divergent improper integrals -- on the other hand -- are limits that either go off to (minus) infinity or end up oscillating.

 

[Fallenleaves]

Improper integrals are limits. Convergent improper integrals are limits that converge to an actual number. Divergent improper integrals -- on the other hand -- are limits that either go off to (minus) infinity or end up oscillating.

Thanks

 

[Ahnfeltia]

@Fallenleaves Have you ever come across this guy? He seems legit, but I can't understand Chinese.
https://www.pornhub.com/model/changhsumath666/videos

 

[Ahnfeltia]

What area of math should I self-study after calculus? @Ahnfeltia @trying to ascend

Linear algebra

 

[Fallenleaves]

@Fallenleaves Have you ever come across this guy? He seems legit, but I can't understand Chinese.
https://www.pornhub.com/model/changhsumath666/videos

I have but I don't like his videos

 

[Ahnfeltia]

I have but I don't like his videos

Fair enough. The concept is hella based tho.

 

[Fallenleaves]

Fair enough. The concept is hella based tho.

https://youtube.com/@blackpenredpen

https://youtube.com/@TheMathSorcerer

I prefer these 2 guys, for now at least

 

[Ahnfeltia]

https://youtube.com/@blackpenredpen

https://youtube.com/@TheMathSorcerer

I prefer these 2 guys, for now at least

I've come across them both. The stuff they tackle is a bit too basic for me.

 

[Fallenleaves]

I've come across them both. The stuff they tackle is a bit too basic for me.

 

[Ahnfeltia]

Have you ever come across <https://www.youtube.com/@MichaelPennMath>? His stuff sounds like it might be right up your alley.

 

[Fallenleaves]

Have you ever come across <https://www.youtube.com/@MichaelPennMath>? His stuff sounds like it might be right up your alley.

Yeah I've seen this video from his channel:

I've recently unsubscribed as most of his content is too advanced for me at this point of time.

 

[Ahnfeltia]

Yeah I've seen this video from his channel:

I've recently unsubscribed as most of his content is too advanced for me at this point of time.

ah ok

 

[Inceldia]

You people are sick.
I have to do a lot of math for school now and it makes me wanna kill myself.
I HATE MATH AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 

[CountBleck]

You people are sick.
I have to do a lot of math for school now and it makes me wanna kill myself.
I HATE MATH AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

i mean, i get it. i thought history was a gay useless subject in high school. i dunno just leave the math nerds to our math

 

[trying to ascend]

You people are sick.
I have to do a lot of math for school now and it makes me wanna kill myself.
I HATE MATH AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

What is the subject?

 

[Inceldia]

i mean, i get it. i thought history was a gay useless subject in high school. i dunno just leave the math nerds to our math

I respect math and high iq mathincels and I know its important for many things but please dont force me to do it
I feel very bad rn and I think it is atleast partially bc of school math.

What is the subject?

Algebra, Vectors, Matrix, population-calculation rn
but after that and a couple other topics I will have to write a big exam on all math things I "learned" fuck my life.

 

[CountBleck]

I respect math and high iq mathincels and I know its important for many things but please dont force me to do it
I feel very bad rn and I think it is atleast partially bc of school math.

yeah it sucks, but i mean you'll get through it then you won't have to think about math anymore

 

[Inceldia]

yeah it sucks, but i mean you'll get through it then you won't have to think about math anymore

I thought this way multiple times and each time it came back to rape my asshole telling me "I aint done with you yet"
I hope this time after I did that exam and passed is truly the last time.

 

[trying to ascend]

I respect math and high iq mathincels and I know its important for many things but please dont force me to do it
I feel very bad rn and I think it is atleast partially bc of school math.

Algebra, Vectors, Matrix, population-calculation rn
but after that and a couple other topics I will have to write a big exam on all math things I "learned" fuck my life.

You will do well bhai.

Are you in college or HS?

 

[Grim_Reaper]

What area of math should I self-study after calculus? @Ahnfeltia @trying to ascend

Linear algebra, differential equations, real/complex analysis, topology.

 

[Inceldia]

You will do well bhai.

Are you in college or HS?

Thanks for the reassuring words bro.
Im not a youngcel, I am redoing some schoolstuff with an online-course.
After I passed the exam(s) I can and will go to university.

 

[Retardinator]

I hate math so much that the existence of this thread pisses me off

 

[trying to ascend]

I hate math so much that the existence of this thread pisses me off

Why you hate math?

 

[Inceldia]

I hate math so much that the existence of this thread pisses me off

same here tbh ngl

 

[Fallenleaves]

here
i wasted 3 minutes overleafing this. if you want solutions just ask for em, but give em a good try first. they aren't easy
View attachment 689619

a) D
b) Converges to 3/4
c) By p value test, it converges to -1/3