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May
9
comment Function whose limit does not exist at all points
@moni94 Your function definition is not valid because the "last digit of the decimal representation" is not defined for every real number. (Take $1/7$ for example.)
May
9
comment How to find the eigenvectors.
@goods Well, you can arbitrarily pick one. The other one will be determined by your first choice.
May
9
answered How to find the eigenvectors.
May
9
comment How to find the eigenvectors.
@goods No. There can be infinitely many pairs that are still orthogonal to the other two.
May
4
reviewed Reject How to proof that bracket of two vector field can be computed by second derivation
May
4
reviewed Approve Result of solving an unsolved problem?
Mar
9
reviewed Reject Express the vector as a sum of two vectors
Mar
8
reviewed Approve How to find union and intersection of these relations?
Mar
8
reviewed Approve Ring Theory and Modules in Norm
Mar
8
comment Eigenvalues for $y''+2y'=\lambda y$
There is no way you can find a closed form expression for $\lambda$. The best way to describe eigenvalues is that they are solutions of the equation $\sqrt{-1-\lambda} = \tan\left(\sqrt{-1-\lambda}\right)$.
Mar
3
comment Trying to find a formula for the following algorithm
What you think shouldn't be correct is in fact correct. The next step is to expand into $\frac 12i^4 + \frac 12i^2$, then compute the sum $\sum_{i=1}^n$ for $\frac 12i^4$ and $\frac 12i^2$ separately.
Mar
3
comment matlab matrix error when computing norm
What is $b^5$ supposed to mean?
Feb
23
comment What to do when particular integral is part of complementary function?
There was nothing magical about the first equation. You can derive it by using the product rule of differentiation on the right-hand side. The remark about change of basis has nothing to do with the derivation.
Feb
22
comment Why does given constraint of n lift when I simplify?
Yes it seems coincidental, but it is not completely unexpected. This kind of phenomenon sometimes leads to an interesting outcome too.
Feb
22
comment Why does given constraint of n lift when I simplify?
$F(1)$ is $a_1 = a_1$, not $a_1 = 1$. $F(1)$ does not say anything about the actual value of $a_1$.
Feb
22
comment Positive partial derivatives implies monotonicity?
It does, by the fundamental theorem of calculus.
Feb
22
comment Why does given constraint of n lift when I simplify?
Just because $n > 1$ implies $F(n)$ (where $F(n)$ is a predicate with variable $n$) does not mean $F(1)$ is not true.
Feb
22
comment Why does given constraint of n lift when I simplify?
The final formula is also valid when $n = 1$.
Feb
22
comment Why does given constraint of n lift when I simplify?
I think "the constraint $n > 1$ is now lifted" means the equation is also valid for $n = 1$, but it does not mean you can use it to find $a_1$. Observe that when you plug in $n = 1$, you get $a_1 = a_1$, which is valid.
Feb
22
comment Series question with unknown limit
You should use the formula $\sum_{n=1}^N n = \frac{N(N+1)}2$.