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Feb
18
comment $ \int_{0}^{2} (2x - x^2)^n dx $ recurrence relation
I still don't see how
Feb
18
comment $ \int_{0}^{2} (2x - x^2)^n dx $ recurrence relation
How do you get to the second row? How is $ -2n \int_o^2 (...) dx $ equal to that?
Feb
25
comment Is the function derivable in $x_0 = 1$?
This uses derivatives and right now we're using the limit definition to computer derivatives and not actually deriving functions, so I can't use this. Even though it is correct
Oct
27
comment Solve $x^2 = I_2$ where x is a 2 by 2 matrix
I'm allowed to work with complex matrices
Oct
21
comment Solve $x^2 = I_2$ where x is a 2 by 2 matrix
sorry, my course in linear algebra doesn't cover those, I was looking for a more simple explanation or solution
Oct
21
comment Solve $x^2 = I_2$ where x is a 2 by 2 matrix
how can i write one of those here?
Mar
14
comment How to compute the sum of every $k$-th binomial coefficient?
I'm in a high school class, we haven't even done integrals and derivatives. There must be a somewhat easier way without requiring FTs.
Mar
14
comment Sum of every $k$th binomial coefficient.
By summing those equations, you would get $(1 + 1)^n + (1+\omega)^n + (1+\omega^2)^n = $ the sum of every third coefficient. But how do you get the closed form on that sum?
Mar
13
comment How to compute the sum of every $k$-th binomial coefficient?
Yes, I noticed that too so perhaps I misunderstood something.
Feb
8
comment How many words can be obtained using 2n letters?
And I assume the same kind of reasoning goes for the generalized case with k letters.
Aug
24
comment Can all Integration and differentiation of a real function form be determined?
I'm sorry, but your question isn't clear. Are you asking if every function defined from a subset of $\mathbb{R}^2$ to $\mathbb{R}^2$ is integrable and differentiable, or if all derivatives/integrales can be expressed in terms of simple functions or about function infinitely-differentiable/integrable? Please clarify what you mean.
Aug
20
comment Derivative of step functions
It was the notion of "distributions" that I was looking for, thanks!
Aug
19
comment Is there a non-contradictory non-trivial axiomatic system in which Gödel's theorem is undecidable?
@Henning Ah yes, that was it, thanks for spotting it!
Aug
19
comment Is there a non-contradictory non-trivial axiomatic system in which Gödel's theorem is undecidable?
@HenningMakholm Ah yes you're right. Then it means that I probably read about another famous theorem that was proved unprovable within ZFC. And Asaf, yes, you're right, thanks, and I originally tagged it as soft as I did not expect a proof or anything very concrete, given the question asked.
Aug
15
comment Derivative of step functions
@JoeJohnson126 Yes, that is what I am asking. And besides that, what is derivative of any individual f (since f is a limit of functions $\lim_{n \rightarrow \infty} f_n(x)$) what is ${f'}_n(x)$ ?
Aug
15
comment Derivative of step functions
Yes, that link illustrates exactly what I mean. With the difference that where I assumed the derivative was infinite, it actually wasn't defined. And this brings me to my question: given that derivative, how can it's integral (Lebesgue or otherwise) be any other value than 0?
Aug
15
comment Derivative of step functions
The derivative of step functions. Because as I said, it seems to me that the classical approach (The one used together with Riemann-Darboux) would yield a derivative with a range of ${0, \infty, -\infty}$.
Aug
15
comment Derivative of step functions
Is it more clear now?
Aug
15
comment How do Taylor polynomials work to approximate functions?
Absolutely awesome visualizations, thanks for the link!
Aug
14
comment Help in understanding integration by changing the variable
And any tips on which to choose as $f(x)$ and which as $g'(x)$ or something?