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SuicideFuel Math thread problem (official)

Ahnfeltia

Ahnfeltia

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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

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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?
 
Ahnfeltia

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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).
 
Fallenleaves

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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

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Why are there 20 bluepillers
 
Caesercel

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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
 
trying to ascend

trying to ascend

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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
 
Last edited:
trying to ascend

trying to ascend

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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)
 
Ahnfeltia

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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

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@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

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

trying to ascend

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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 :feelsokman:
 
Ahnfeltia

Ahnfeltia

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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

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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

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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 :feelsokman:
 
Ahnfeltia

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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

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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

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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

trying to ascend

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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

Inceldia

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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:cryfeels:
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 :feelsrope:
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

CountBleck

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I respect math and high iq mathincels and I know its important for many things but please dont force me to do it:cryfeels:
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

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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

trying to ascend

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

Algebra, Vectors, Matrix, population-calculation rn :feelsrope:
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

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What area of math should I self-study after calculus? @Ahnfeltia @trying to ascend
Linear algebra, differential equations, real/complex analysis, topology.
 
Inceldia

Inceldia

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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

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

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