Recent content by Horseboy

Like the title says, this is about the logistic equation. It's a well known model of population growth. How "r" and "K" affect it is given in the most basic understanding of the model. I've given you just as much information as I've received. "r" and "K" are obviously constants, just as lambda...

Homework Statement I need to write \begin{align*} N_{k+1} = \frac{\lambda N_{k} }{1+aN_{k} } \end{align*} in the form \begin{align*} N_{k+1} = N_{k} + R(N_{k})N_{k} \end{align*} Homework Equations As above The Attempt at a Solution I know that \begin{align*} N_{k+1} = N_{k} +...

I think I've actually done a relatively ok job, kinda makes sense, handing all the stuff in now. I'll be keen to see the tutor's answers when they post them, I'll put them here for future viewing. Thanks all for the help, I'll be back :) I'll post what I wrote up a bit later.

Wow, thanks for all the effort guys. I had a nap as I was crashing bad :P Thought a fresh brain might do a little better. So PeroK, essentially you're saying that using estimates, you're able to condense that big equation down to just |x|? And also I looked up that min() trick you were...

\begin{align*} \sqrt{x^2+(y-1)^2} < \delta \implies \left|x^2y\right| < \epsilon \end{align*} \begin{align*}If \space \delta = \frac{1}{2}, \space then \space\left|x^2\right|<\frac{\delta}{2}, \left|y\right| < \frac{3}{2} \end{align*} \begin{align*} \left|x^2y\right| < \frac{3\delta}{4} =...

I actually thought about this at the very start! Knew it was a good lead! It definitely looks a lot easier, but of course using my method of subbing in delta for the appropriate variables (δ>|x| and δ>|y-1|), I get the same answer of \begin{align*}δ^3 + δ^2 \end{align*} as 1/2 can just be...

Thanks guys, I do apologise, I've been stuck on this question for the last 3 days and I'm forgetting that not everyone just automatically knows what I'm talking about ^^; Didn't even specify the question correctly! Yes PeroK, you are correct, that is what I'm trying to show. I'm really...

The problem is that it's confusing for me, and I'm unable to progress. If \begin{align*} \epsilon = \left| \frac{\delta^3+\delta^2}{2} \right| \end{align*} then \begin{align*} \epsilon = \frac{1}{2} \delta^2 \left( \delta + 1 \right) \end{align*} so \begin{align*} \epsilon = 0, 1...

Homework Statement Apply the definition of the limit to show that \begin{align*} f(x,y) = \frac{x^2\,y\,\left( y - 1 \right) ^2 }{x^2 + \left( y-1 \right) ^2 } = 0\end{align*} I know I'm required to use the epsilon delta method here, no polar stuff either, just straight at it. Homework...