Recent content by msell2

I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...

What is wrong with that inequality?

Thanks for the help! Does this look right? Given ε>0 we can determine an N\inN so that |an-L|<ε for n≥N. We have: |an-L|=|\frac{n^{2}}{2n^{2}+n-1}-\frac{1}{2}|=|\frac{2n^{2}}{2(2n^{2}+n-1}-\frac{2n^{2}+n-1}{2(2n^{2}+n-1}|=|\frac{-n+1}{2(2n^{2}+n-1}|=|\frac{-n+1}{2(2n-1)(n+1)}|<ε. Now take...

Homework Statement Prove the following sequence {an} converges to L=1/2 an = n2/(2n2+n-1) The Attempt at a Solution Given ε>0 we can determine an N∈N so that |an - L|<ε for n≥N. We have: |an-L|=|(n2/(2n2+n-1)-(1/2)| = |(-n+1)/(2(2n-1)(n+1))| I'm not sure what to do once I get to this...

Homework Statement Suppose that we use a Michaelis-Menten growth rate in the chemostat model, and that the parameters are chosen so that a positive steady state exists. Show that N = f(V,F,C0) = (C0(F - VKm) + FKn)/(a(F - VKm)) and C = (FKn)/(F - VKm) at the positive steady state. The...

Assume that f is continuous on [a,b] and differentiable on (a,b). Assume also that f′(x) ≠ 0 on (a,b) and f(a) and f(b) have different signs. Show that the equation f (x) = 0 has a unique solution in (a, b). I'm not really sure how to even start this proof. Do I need to use the...

(d4x)/(dt4) + (1/(1+t))*(d2)/(dt2) = x(t) Is this differential equation linear or non-linear? I don't understand the difference.

Homework Statement Determine all fixed points of: dx/dt = x(β-x-ay) dy/dt = y(-1+ax-y) β and a are parameters. I get what to do when there is just one differential equation, but not two.

I get what I need to do in theory, I just don't actually know how to do it. How do you find v such that (λI-A)v=0?

[0 1] [-2 -2] This is the 2x2 matrix. [λ -1] [2 λ+2] This is the matrix that equals λI - A. Here are the eigenvalues I found: λ = -1 + i, -1 - i I am really confused at what to do next to find the eigenvectors. I keep looking online for help but I still can't figure it...

So everything is the same even though there are vectors?

x(t) = (Cv + D(tv + w))e^(λt) x'(t) = ? C, D, λ are constants x(t), v, w are vectors (v is an eigenvector, w is a generalized eigenvector) t is the variable This is coming from a larger question, asking to prove that the above equation satisfies x'(t)=Ax(t), where A is a 2x2 matrix and...