Inequality Definition and 1000 Threads

Homework Statement Digital filter analysis - this is just one part of a multi-part question I can't move forward with. It's supposed to be an auxilliary question and isn't the "meat" of the problem. Find b, such that maximum of the magnitude of the frequency response function...

Hello to everyone. This is my first time here so I hope I will not cause any unwanted trouble. Straight to the problem. I have one inequality for which I would like to prove, but I do not know how. The inequality has the following form:- (1+a)q < q/(1-a), where a < 1 and q can be any positive...

Homework Statement The problem is: for all 0≤a≤1 so i need to find the domain Homework Equations N/A The Attempt at a Solution I tried it like this: yet my solution is wrong,i am not so sure why. wolfram gives me this;

Write as one inequality with an absolute value x<-5 or 8<x not sure how you introduce the absolute value in this to solve it. thanks ahead

Homework Statement Prove the triangle inequality for the following metric d d\big((x_1, x_2), (y_1, y_2)\big) = \begin{cases} |x_2| + |y_2| + |x_1 - y_1| & \text{if } x_1 \neq y_1 \\ |x_2 - y_2| & \text{if } x_1 = y_1 \end{cases}, where x_1, x_2, y_1, y_2 \in \mathbb{R}...

Homework Statement Find all x for which \frac{x-1}{x+1}>0 \qquad(1)Homework Equations (2) AB > 0 if A,B >0 OR A,B < 0 (3) 1/Z > 0 => Z > 0 The Attempt at a Solution Since (1) holds if: (x-1) > 0 \text{ and } (x+1) > 0 \qquad x\ne -1 then we must have x>1 AND x>-1 and since (1) also...

Homework Statement I am doing the HW in Spivak's calculus (problem 4 (ii) ) on inequalities. The problem statement is: find all x for which 5-x2 > 8The Attempt at a Solution I know this is a simple problem, but bear with me for a moment. I want someone who is familiar with Spivak to tell...

Homework Statement Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|. Homework Equations The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and...

Hi everyone I don't know if I can find someone here to help me understand this issue, but I'll try the jensen inequality can be found here http://en.wikipedia.org/wiki/Jensen%27s_inequality I have the following discrete random variable X with the following pmf: x 0...

I may have posted this back in the Old Country, but: let the polynomial: \[P(x)=x^n+a_1X^{n-1}+ ... + a_{n-1}x+1 \] have non-negative coeficients and \(n\) real roots. Prove that \(P(2)\ge 3^n \) CB

Prove that for positive real numbers a,b (a+1/b+1)^(b+1) is greater than or equal to (a/b)^(b). The case in which a<b is easy to prove, but after trying to represent the inequality with an integral, I'm a bit stumped. Any ideas?

Find all numbers x for wich: x+3^x<4 Relevant equations (PI) (Associative law for addition) (P2) (Existence of an additive identity) (P3) (Existence of additive inverses) (P4) (Commutative law for addition) (P5) (Associative law for multiplication) (P6) (Existence of a multiplicative identity)...

I am puzzled about this simple case, Suppose we have (A+B)T(A+B) <= (A+B1)T(A+B1), Can we say something about the relation between BTB and B1TB1? For example, is it correct if I say BTB <= B1TB1?

I'm trying to absorb a perplexing proof of Young's inequality I've found. Young's inequality states that if A,B \geq 0 and 0 \leq \theta \leq 1, then A^\theta B^{1-\theta} \leq \theta A + (1-\theta)B. The first step they take is the following: We can assume B \neq 0. (I get that.) But then...

The problem and my question and thoughts are all in the picture.

I found this problem the other day, seems interesting but I am still not sure about the solution Anybody can help x, y, z are numbers with x+y+z=1 and 0<x,y,z<1 prove that sqrt(xy/(z+xy))+sqrt(yz/(x+yz))+sqrt(xz/(y+xz))<=3/2 ("<=" means less or equal)

Homework Statement Let 1\leq p,q that satisfy p+q=pq and x\in\ell_{p},\, y\in\ell_{q}. Then \begin{align} \sum_{k=1}^{\infty}\left\vert x_{k}y_{k}\right\vert\leq\left(\sum_{k=1}^{\infty}\left\vert x_{k}\right\vert^{p}\right)^{\frac{1}{p}}\left( \sum_{k=1}^{\infty}\left\vert...

I am confused by the role of photon polarisation in Bell inequality experiments. The original logic of EPR as I understand it is based on the HUP such that QM predicts that measurement of momentum on one particle should affect the measurement of position of the other particle. Yet across...

I posted the paragraph with the inequality where I am confused... I also added a portion i highlighted in red

Homework Statement Use the Cauchy-Schwarz inequality to prove that for all real values of a, b, and theta (which ill denote as θ), (a cosθ + b sinθ)2 ≤ a2 + b2 Homework Equations so the Cauchy-Schwarz inequality is | < u,v>| ≤ ||u|| ||v|| The Attempt at a Solution I'm having...

Homework Statement Let u = [a b] and v = [1 1]. Use the Cauchy-Schwarz inequality to show that (a+b/2)2 ≤ a2+b2/2. Those vectors are supposed to be in column form. Homework Equations |<u,v>| ≤||u|| ||v||, and the fact that inner product here is defined by dot product (so <u,v> = u\cdotv)...

is \frac{x-1}{x}<ln(x)<x-1 valid for 0<x<1 I think it is I just want to get a second opinion.

Showing the inequality holds for an interval (?) Homework Statement Hi, my homework question is: Show that the inequality \sqrt{2+x}<2+\frac{x}{4} holds \forallx\in[-2,0] Homework Equations The Attempt at a Solution I tried using IVT or bisection method, but they are just for...

I've been reading a book called Superfractals, and I'm having trouble with a particular proof: Definitions: The distance from a point x \in X to a set B \in \mathbb{H}(X) (where \mathbb{H}(X) is the space of nonempty compact subsets of X is: D_B(x):=\mbox{min}\lbrace d(x,b):b \in B\rbrace The...

Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...

Homework Statement Please see below... Homework Equations Please see below... The Attempt at a Solution Hi. This question is on geometry with circle and triangle. I am stuck only on 2 parts of the solution and not the whole solution... Thank you...

Is there a way to do this without differentiation? \left(a+b\right)^{p} \leq a^{p}+b^{p} 0<p<1 and a,b\geq 0 pulling the a out of the the first part and dividing by it to get \left(1+\frac{b}{a}\right)^{p}\leq 1+\frac{b}{a}^{p} This seems like the way to go but am stuck. Any...

In an example in my textbook, it says the following: "If -1 ≤ x ≤ 1, then 0 ≤ x2 ≤ 1. " Can someone explain to me how to move from the first statement to the second statement please? I'm not quite sure how the -1 turned into a 0...

Homework Statement Prove that \sum_{k=0}^n {3k\choose k}\ge \frac{5^n-1}{4}Homework Equations {3k\choose k}= \frac{(3k)!}{k!(2k)!}The Attempt at a Solution I tried using the induction principle, but... Here my attempt: For n=0 1>0 ok Suppose that is true for n, i.e.: \sum_{k=0}^n...

Hello Friends, I at a loss to understand the parts of the following proof: For any positive ineteger n, prove that: (1+1/n)^n < (1+1/n+1)^n+1 a, b positive real numbers such that a < b Proof: b^n+1 - a^n+1 = (b-a)(b^n+ab^n-1+...+a^n) I could not understand the following part: By...

This may seem trivial, but for some reason I am having trouble with it. For a and b in the complex plane, I am trying to prove the following: |a|^2+|b|^2 >= |(a+b)/2|^2 I need this for part of a larger proof.

Homework Statement I already have the solutions, but I am not sure what the solutions are trying to say. http://img194.imageshack.us/img194/2595/unledlvc.jpg So in I don't understand this, we have n > \frac{1}{\epsilon} and If (and I am guessing we really want this to...

Homework Statement Determine the set of positive values of x that satisfy the following inequality: (1/x) - (1/(x-1)) > (1/(x-2)) a) (0, 1) union (2^1/2, 2) b) (0, 1/2) union (1, 2) c) (1/2, 1) union (2^1/2, 2(2^1/2)) d) (0, 2^1/2) union (3/2, 2) e) (1, 2^1/2) union (2, 2(2^1/2))...

In this link is a part of a book on approximations of functions. http://books.google.com/books/about/An_Introduction_to_the_Approximation_of.html?id=VTW2cmjC43YC I'd be thankful if someone would explain how the inequality near the top of page 17 was gotten.

Homework Statement So these were introduced in my lecture and I'm not really clear what they do or why it's true or when they're useful. Can you please explain them to me in a simple way? Thank you.Homework Equations Markov's Inequality: If X is a non-negative random variable, (that is, P(X...

Homework Statement Why is \langle p^2\rangle >0 where p=-i\hbar{d\over dx}, (noting the ***strict*** inequality) for all normalized wavefunctions? I would have argued that because we can't have \psi=constant, but then I thought that we can normalize such a wavefunction by using periodic...

Homework Statement Determine the values of z \in \mathbb{C} for which |z+2| > 1 + |z-2| holds. Homework Equations Nothing complicated I can think of. The Attempt at a Solution For real values this holds for anything greater than 1/2. If I could figure out the boundaries of the...

a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1. Then prove that \left( a+\dfrac{1}{b}\right).\left(b+\dfrac{1}{c}\right).\left(c+\dfrac{1}{a}\right)\geq \left(\dfrac{10}{3}\right)^3 Anyone an idea on how to start with this exercise?

Young's Inequality can be restated as: s^(x)t^(1-x)<=xs + (1-x)t where s,t>=0 and 0<x<1. Basically I've been asked to prove this. I've been fiddling about with it for a couple of hours to no avail. I've tried to substitute t=e^u and s=e^v and then use partial differentiation w.r.t to...

Homework Statement What I want to show is this: ∫|x+y| ≤ ∫|x| + ∫|y| Homework Equations |x+y| ≤ |x| + |y| The Attempt at a Solution So I thought if I used the triangle inequality I could get to something along the lines of: Lets g belong to the real numbers ∫|x+y| =...

Hello all, the problem I have is the following: Suppose f \in C^1(0,1) and f(0) = 0, then f^2(x) \le \int_0^1 f^2(x) dx, but I was wondering if 1 is the best constant for the inequality. In other words, how do I determine the best bound for f^2(x) \le K \int_0^1 f^2(x) dx...

Homework Statement Suppose that w is a complex number which is not both real and \left\lfloorw\right\rfloor\geq1 (the absolute value of w). Verify that Re[(1-w^{2})^{1/2}+iw]>0. Homework Equations The Attempt at a Solution I attempted to solve this problem by dividing it into...

Homework Statement 2x-1 _____ > 0 5x+3 Homework Equations The Attempt at a Solution Just wondering, my teacher taught us that youre only supposed to look at what makes the denominator = 0, and don't look at the numerator because it has no affect on anything. So, if i...

Can Someone please solve this inequality! Homework Statement ((2x)3^x)/(x+1) < 0 Thanks is advance! Homework Equations The Attempt at a Solution

Homework Statement Show that if a_n > 0 for all n, \liminf{\frac{a_{n+1}}{a_n}} \leq \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \leq \limsup{\frac{a_{n+1}}{a_n}}Homework Equations \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \liminf{\frac{a_{n+1}}{a_n}} \leq \limsup{\frac{a_{n+1}}{a_n}} These...

Homework Statement This is part of a question on absolute convergence on series. The following equation is given as a hint. It says that before answering the question on series I should prove that |xy| <= 1/2(|x|^2 + |y|^2) for any x,y ε R Homework Equations The Attempt at a...

Homework Statement > a[1], a[2], a[3], .. , a[n] are arbitrary real numbers, prove that; abs(sum(a[i], i = 1 .. n)) <= sum(abs(a[i]), i = 1 .. n) Homework Equations The Attempt at a Solution I have uploaded my attempt as a pdf file, since I'm not too familiar with the...

p<q, r<s, and r<q. Which of the following statements must be true? I. p<s II. s<q III. r<p The correct answer could be either one statement, a combination of statements, or none of the statements. Came across this question while helping some high school students prepare for their SATs...

Homework Statement 4x5-16x4+9x3+23x2-15x-9 > 0 Homework Equations Synthetic division PQ Rule? The Attempt at a Solution Don't know how or where to begin

Hello I am doing a calculus proof with epsilon-delta and I am trying to say the following: -1\leqsin x\leq1 and now I want to get (sin x )^2 ...so can you just square all sides of the inequality like this: (-1)^2\leq(sin x)^2\leq(1)^2 ?? According to the rule for inequalities...