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Jan
9
comment Rate of convergence in an infinite geometric series of matrices
@Paulo no problem.
Jan
3
comment Find $k$ such that the vector with $w_n=1/(1+a_n k)$ is orthogonal to a given vector
@emanuele Not a general one, unfortunately. There are ones for $N=2,3,4$. Why not be happy with a numerical one?
Jan
2
comment Solution verification: solving $\sqrt{x-4}-\sqrt{x-5}+1=0$
@RealHilbert We are not dealing with complex curves, there are no branches. $\sqrt{x} > 0$ by definition...
Jan
2
comment Solution verification: solving $\sqrt{x-4}-\sqrt{x-5}+1=0$
@RealHilbert If you plug in any real value for $x$ into $\sqrt{(x-5)(x-4)}$, you will never get anything negative out...
Jan
2
comment Solution verification: solving $\sqrt{x-4}-\sqrt{x-5}+1=0$
$$(\sqrt{x}-1)^2 = x - 2\sqrt{x} + 1$$ and you seem to have dropped the 2...
Jan
2
comment Are the 2nd order linear differential equations vector space?
@B.S. agree, forgot to mention, thank you
Jan
2
comment How find this $\lim_{n\to\infty}a_{n}$
wolframalpha.com/input/?i=a%5Bn%5D+%3D+RoundUp%5B2*pi%2Fa%5Bn-1%5D%5D‌​*a_%5Bn-1%5D-2*pi%2C+a%5B1%5D+%3D+2*pi-6
Jan
2
comment How to obtain a pdf of a random variable defined as a function of many variables?
@Did thanks for the edit
Jan
2
comment Finding limit by l'hospital rule.
wolframalpha.com/input/?i=x%5E3%20*Arctan%5Bx%5D&t=crmtb01 for more info
Jan
2
comment Finding limit by l'hospital rule.
Are you saying $A, B$ are independent of $x$? Then $A=B=0$ seems like the only possibility, but $x^3 \tan^{-1} (x)$ does not converge I believe
Jan
2
comment Probability of picked cards to be smaller than the largest picked card
@Henry likely just put it down as the first in a pile...
Jan
2
comment Probability of picked cards to be smaller than the largest picked card
What does probablistic equations mean in this context? Expected values of quantity in each pile?
Jan
2
comment Which Expression of e Converges Fastest?
... and is much quicker to compute using Hermite evaluation
Jan
2
comment Find $k$ such that the vector with $w_n=1/(1+a_n k)$ is orthogonal to a given vector
@emanuele Lots of people ask questions here without any clue as to what the definitions mean. I am glad you understand. So for each $N$ you must find roots of a polynomial of degree $N$ to get the values. E.g. no guarantees for $N=1$, and $$ -\frac{v_1+v_2}{v_1 a_2 - v_2 a_1} $$ for $N=2$. So you can possibly find more analytical solution for $N=3,4$ but no more than that.
Jan
2
comment Prove that: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1$
Thanks, Ehsan - I was wondering why it was tagged abstract-algebra...
Jan
2
comment Are the 2nd order linear differential equations vector space?
Hi, Arash, welcome to Math.SE! Using MathJax to edit your formulae would be a real help... Does this require the homework tag as well?
Jan
2
comment Do I calculate it right for the hypothesis testing?
Looks very reasonable to me.
Jan
2
comment Evaluating sign of inequality under constraint
@tomka What is more interesting is to find the entire range of values of $a$ where it is true and false...
Jan
2
comment Evaluating sign of inequality under constraint
for some real $a$? Try $a=0$ :-). Do you mean for any real $a$?
Jan
2
comment Deciding whether this integral is convergent or divergent: $\int_1^\infty \frac{e^{\sqrt {x}}}{\sqrt{x}}\,\mathrm dx$
@Pumpkin if you sub correctly your integral becomes $\int e^{-y}$...