Recent content by Cristopher

Just in case anyone is interested, today someone posted an excellent proof of why the Stirling transform of (k-1)! is (-1)^n \operatorname{Li}_{1-n}(2) here: http://math.stackexchange.com/questions/1348593/stirling-transform-of-k-1

I want to evaluate \displaystyle\lim_{(x,y)\to(-1,0)}\frac{y^4(x+1)}{|x+1|^3+2|y|^3} With some help, I was able to prove that the limit is 0, using Hölder's inequality. Like this: \left(|x+1|^3\right)^{1/5}\left(\frac{1}{2}|y|^3\right)^{4/5}\leq\frac{1}{5}|x+1|^3+\frac{4}{5}\frac{1}{2}|y|^3...

While reading about combinatorial mathematics, I came across the Stirling transform. https://en.wikipedia.org/wiki/Stirling_transform So then, if I want to find the Stirling transform of, for instance, ##(k-1)!##, I have to compute this (using the explicit formula of the Stirling number of the...

Thank you all. Yes, I also thought that it says that the limit as x→+∞ and as x→-∞ are the same. Indeed, I did look at the graph of the funcion x sin(1/x) before asking, and these limits are both equal to 1. I also noticed there's symmetry in the graph, I thought it may have something to do...

I came across something I'd never seen before, the use of |x| instead of just ‘x’ in limits. What is the difference between \displaystyle\lim_{|x|\to\infty}x\sin\frac{1}{x} and \displaystyle\lim_{x\to\infty}x\sin\frac{1}{x} ? Is there any difference when evaluating them? Is that notation used...

Lavinia and HallsofIvy, forgive my ignorance, but I didn't know ln(x) could be definied in many ways. If the definition I'm using is so important, I don't know why I haven't been asked this before. I was taught that ln(x) is a function so that \displaystyle\ f: (0, \infty) \rightarrow...

I'm not sure if I understand your question correctly, but I was referring to the natural logarithm, with base e.

Thank you all for your answers! Thank you ;) I knew I would probably have to use those properties but I never thought of writing 1/h as an exponent! DonAntonio's post made me realize that I can actually make the indeterminate form 0/0 into 1∞. The properties ln(a)-ln(b)= ln(a/b) and...

Hi. I know that the derivative of ln(x) is 1/x but I can't seem to find a way to calculate this using this limit ^{lim}_{h→0}\frac{ln(x+h)-ln(x)}{h} Could anyone give me a hand on how to find derivative of lnx? :) Thanks!