Upper bound Definition and 109 Threads

Dear All, I am searching for an upper bound of exponential function (or sum of experiential functions): 1) \exp(x)\leq f(x) or: 2) \sum_{i=1}^n \exp(x_i) \leq f(x_1,\cdots,x_n, n) . Since exponential function is convex, it is not possible to use Jenssen's inequality to get an upper bound...

I'm having a little difficulty understanding Epsilon in the definition of convergence. From what the book says it is any small real number greater than zero (as small as you can imagine?). Also, since I don't quite grasp what this epsilon is and how it helps define convergence, I am having...

This paper states that: This means that the upper bound of computability is "10^{120} ops on 10^{90} bits." Question: does this upper bound apply to quantum computers as well?

The converse of the Upper Bound Theorem would state that a graph which satisfies the inequality e \leq { \frac{n (v-2)}{n-2} is planar. This converse is not true as seen in picture. Verify that the inequality e \leq { \frac{n (v-2)}{n-2} is true for this graph. Using the...

Let S = \{x | x \in \mathbb{R}, x \ge 0, x^2 < c\} Show that c + 1 is an upper bound for S and therefore, by the Completeness Axiom, S has a least upper bound that we denote by b. Pretty much the only tools I've got are the Field Axioms. I think I'm supposed to do something like: x2 \ge 0...

Obtain an upper bound for the optimal value in the following problem; Max (4x_1 + x_2 + 2x_3 + 3x_4 ) 2x_1 - x_2 + x_3 - 2x_4 <= 2 7x_1 + x_2 + 5x_3 + 10x_4 <= 4 2x_1 + 3x_2 - x_3 - x_4 <= 2 x_i >= 0 , i= 1,2,3,4 any hint.help. please. thanks note: >= means > or equal to <= means <...

Dear members, I try to find the upper bound of the following function. Can anybody gives a hint? Thanks! f(t,p)=\sum_p \frac{p(1-p)}{t^5}[p^4(9t^4-81t^3+225t^2-274t+120)+p^3(-12t^4+129t^3-400t^2+524t-240)+ \mbox{\hspace{2cm}}p^2(4t^4-59t^3+...

Hey guys, I have a sequence, \sqrt{2}, \sqrt{2 \sqrt{2}}, \sqrt{2 \sqrt{2 \sqrt{2}}}, ... Basically, the sequence is defined as x1 = root 2 x(n+1) = root (2 * xn). I need to show that this sequence converges and find the limit. I proved by induction that this sequence increases...

I need some help with a question. Q) Prove that (2n^4 + 4n^2 + 3n - 5)/(n^4 - n^3 + 2n^2 - 80) converges to 2 as n goes to infinity. A) By the algebra of limits, this converges to 2 since lim(n->oo)[2 + 4/n^2 + 3/n^3 - 5/n^4]/lim(n->oo)[1 - 1/n + 2/n^2 - 80/n^4) (2 + 0 + 0 + 0)/(1...