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SuicideFuel Math thread problem (official)

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


r = 3/4R.

P = weight of each sphere.

Find the value of the weight of the cylinder, such that the system is at rest
 
a) it actually converges to 0.
b) it actually converges to 1/4
c) it converges to pi/4. not -1/3.
Why can't we approximate the integral of part c to be 1/x^4
 

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