1. ### How would I prove that ln (lim (u)) = lim (ln (u))

Thanks again!
2. ### How would I prove that ln (lim (u)) = lim (ln (u))

Thanks for the answer! However, I do not get the step where ln(limn→∞ un)=limn→∞ ( ln(un)). How did you change the order of the natural log and the limit?
3. ### How would I prove that ln (lim (u)) = lim (ln (u))

We were working with L'hospital's rule and my teacher said that the teacher before him told him that this was true: lim (x→∞) [ln u] = ln ( lim (x→∞) u), where u is a continuous function. My teacher has never found a proof for this, although it works every time. Does anyone know how to...
4. ### Why is the salt solubility curve flat?

I know most salts' have increased solubility in 100g of water with an increase in temperature, a few have an inverse relationship, but why does NaCl flatline regardless of temperature? Like is there a mechanism that explains this phenomenon? Thanks in advance.
5. ### Proof for tabular integration?

Today we learnt tabular integration as a shortcut method for integration by parts. Is there a proof that legitimizes tabular integration out there, or some general formula? Because there has to be some sort of logic for the process of creating the diagonal lines, or assigning pluses and minuses...
6. ### Spacetime for an anti-black hole?

So we often see visualizations of what the space time curvature of a black hole looks like, as in a funnel. http://www.astrosociety.org/pubs/mercury/9802/images/embedding.gif [Broken] But are there any predictions or observations of space time curvature looking like a really steep mountain...
7. ### Inverse Chi Square?

Hey all: I just found out that the question I was asking required the use of a table of corresponding X^2 statistics and their probabilities (which I was not given). Thanks for your time anyway.
8. ### Inverse Chi Square?

How can I determine what the smallest value of a χ2 statistic must be to reject the null hypothesis at α = 5%, for a distribution with 9 degrees of freedom? Thanks in advance.
9. ### What is Euler's identity really saying?

So it is true that ei∏+1=0. But what does this mean? Why are all these numbers linked?
10. ### Is this system random or not?

I guess that solves it. Thanks all.
11. ### Is this system random or not?

Hey dcpo and Office-Shredder: Perhaps I am just paranoid about not using functions in this context. I cannot think of a way to avoid using a function and yet still maintaining the randomness of an element of a domain assumed to be random when introducing the bit about adding a 1. On a side...
12. ### Is this system random or not?

Hey dcpo: Ohh. So if the process of generating a random number includes adding 1 to it, it is non deterministic? So there really is no function involved, like the Y = X+1 like my friend was saying? Also, just curious, what is your definition of randomness? Thanks again.
13. ### Is this system random or not?

Hey dcpo: So, to see if I understand, if you have a random number and add one to it, even though we are applying an operation to that random number, the resulting number is not determined by the first one? Because then could we not subtract one from the resulting number and arrive at the...
14. ### Is this system random or not?

What I mean to say, in response to dcpo, is that if f(x) is not a random process, then isn't f(any random x) not random? Because aren't we choosing what we are feeding into the function, albeit via a random process, which makes the range determined? I do not understand how randomness and...
15. ### Is this system random or not?

So if a random process is not a function, then is the f(x)= x+1 a random process? Please tell me more :)