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1. ### Calculus Derivative Terminology

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...
2. ### Proving Limit with Epsilon and Delta

What is wrong with that inequality?
3. ### Proving Limit with Epsilon and Delta

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...
4. ### Proving Limit with Epsilon and Delta

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...
5. ### Dynamic System: Chemostat Variation

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...
6. ### Unique Solution Proof

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...
7. ### Linear or Non-Linear Differential Equations

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

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.
9. ### Meet in the middle attack on 2DES

What is the probability that the meet in the middle attack on 2DES where the attacker knows three plaintexts and corresponding pairs of ciphertexts will succeed? I get how the meet in the middle attack works when the adversary just knows 1 plaintext and ciphertext, but I do not understand...
10. ### Cryptography definition

Prove that the following definition cannot be satisfied if Π can encrypt arbitrary-length messages and the adversary is not restricted to outputting equal-length messages in experiment PrivKeavA,∏. A prive-key encryption scheme ∏=(Gen, Enc, Dec) has indistinguishable encryptions in the...
11. ### How do you find this eigenvector?

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?
12. ### How do you find this eigenvector?

[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...
13. ### How do you take this derivative?

So everything is the same even though there are vectors?
14. ### How do you take this derivative?

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...