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Jul
1
answered How do you show that $\displaystyle\lim_{x\to 0}\frac{\sin(x)}{\sqrt{x\sin(4x)}} $does not exist?
Jul
1
comment Find two linearly independent solutions of a Legendre equation about $x=0.$
Yep. I think $1-x^2$ is not a solution.
Jul
1
comment Find two linearly independent solutions of a Legendre equation about $x=0.$
For part (a), you have no condition on either $a_0$ or $a_1$. They are therefore independent of each other. So your expression is actually two solutions in one already. Congratulations!
Jun
30
accepted probability of exactly one out of N events occuring
Jun
30
comment probability of exactly one out of N events occuring
I have seen something like this, but honestly don't understand it. I guess this has something to do with "generators"? Do you have a reference? Thanks.
Jun
30
comment probability of exactly one out of N events occuring
@Archaick I was typing too fast and making too many mistakes. The probability for all events is $1/i$. So the first event is guaranteed to happen.
Jun
30
revised probability of exactly one out of N events occuring
typo
Jun
30
asked probability of exactly one out of N events occuring
Jun
22
answered Divergence of $\vec{F} = \frac{\hat{\mathrm{r}}}{r^{2}}$
Jun
19
comment Deriving basic form of sine wave
$\sin()$ and $\cos()$ are equally fundamental. There's no advantage in deriving $\sin()$ from $\cos()$ over $\cos()$ from $\sin()$, unless you just have an assignment where you are told to do that. If you understand the relationship between them, you're already there.
Jun
18
comment Explain how the proof is done
In answer to your first question, when you multiply by $A$, you get an equation that has $A^3$ in it. But you already know $A^3$ from eq. (i), so just substitute it in.
Jun
17
comment Number of graphs such that two sides remain connected after some edges are removed
This reminds me of some renormalization problems I have seen. You might try googling "renormalization". Apologies if you already knew that.
Jun
16
answered Prove that the co-ordinates of the centroid of a triangle is an average of that of vertices
Jun
16
comment Changing complex eigenvalues to real eigenvalues given a $2 \times 2$ matrix and a characteristic equation
Well, if it makes you feel any better, I get the same answer as you.
Jun
4
comment Two Dice Question: If at least one is a $2$, what is the probability both are $2$?
If anyone cares, apologies for my now deleted answer. I misread "At least one of the dice is 2" as "One of the dice is 2." Will be more careful next time.
Jun
3
answered Probability of person having A if person also owns B
May
27
comment Solution to the 1-D heat equation
I'm getting fussed at by the site moderator. This will be my last comment. Yes, I mean $u_x$.
May
27
comment Solution to the 1-D heat equation
No, but setting the derivatives to zero on the boundaries does imply your integral. There might be several other artificial ways to satisfy your integral, like putting a "source" term on one boundary. Setting derivatives to zero is simplest.
May
27
comment Solution to the 1-D heat equation
Your integral does imply mass conservation. Your boundary conditions $u(0,t)=u(L,t)=0$ guarantee that there will not be mass conservation. There is a contradiction.
May
27
comment Solution to the 1-D heat equation
If you solve it with the boundary conditions you mentioned, you will absolutely not conserve mass because all the mass will slowly dribble out the ends of your domain. There is no way to fix this without changing the boundary conditions. Changing conditions so that the derivatives of $u$ are zero on the boundaries, or so that the boundary is periodic, would do it.