Inequalities Definition and 329 Threads

Homework Statement Given an algorithm A i need to figure out a formula that can be used to prove that the algorithm is O(logN). I will try to avoid the details of the algorithm, since i need help with the math only. I think all you need to know is that A takes two arguments i and j. So you...

Homework Statement I'm looking for help in proving a few quantum mechanics inequalities. I can't really get started on any of them, so just a few general tips would be helpful. For example: Given a complete set of normalized discrete eigenstates |n> with eigenvalues q_n. For any observable P...

Homework Statement find all values of x in the interval [0, 2pi] that satisfy the equation 2cosx + 1 less than or equal to 0 Homework Equations None. The Attempt at a Solution for when 2cosx+1=0 cosx=-1/2 x= 2pi/3, 4pi/3 but what about the values for when 2cosx + 1 is less then...

how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables? eg; |x| + or - |y| =, >, <, a

Homework Statement Quick question on Rational Inequalities.. Say I have \frac{1+x}{1-x} \huge\geq 1 Why can we not multiply 1 by denominator (1-x) is this because if x > 1 then (1-x) would be negative in effect changing the sign of the inequality.. but if x<1 then the...

Homework Statement tanx + 3cotx = 4 Homework Equations The Attempt at a Solution Heres my attempt: tanx + 3/tanx - 4 = 0 (tan^2x -4tanx + 3) / tanx = 0 tan^2x - 4 tanx + 3 (tanx - 3 ) (tanx - 1 ) = 0 tan = 3, tan = 1 im not sure about tan = 3, but for tan = 1 ...

Homework Statement "There is a very useful way of describing the points of the closed interval [a,b] (where we assume, as usual, that a < b) a. Consider the interval [0,b]. Prove that if x is in [0,b] then x = tb for some t with 0 <= t <= 1. What is the significance of the number t? What is...

Homework Statement 1. x-2|x| < 3 Homework Equations The Attempt at a Solution Okay, I attempted this equation below but I don't know if I'm right. x-2|x|- 3 < 0 x^2 - 2x - 3 < 0 (x - 3) (x + 1) < 0 x = 3 x = -1

Homework Statement Solve (x+2)/(x+1) -2 < 0 Homework Equations LCD: x + 1 The Attempt at a Solution (x+2-2x-2)/(x+1) < 0 (-x )/(x+1) < 0 But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.

Homework Statement 1. 9x^2 + 12x + 4 ≥ 0 2. 2 - 5x - 3x^2 ≤ 0 Homework Equations The Attempt at a Solution 1. Can't you factor this into (3x + 2) (3x + 2)? 2. Looking at this inequality, I am thinking if you can change this inequality into 3x^2 + 5x + 2.

Homework Statement I solved the problem and it matches the answer at the end of the book. Please explain why am I right? Why these two answers are correct? THank you Homework Equations The Attempt at a Solution

Homework Statement The problem and my half solution is given. How do I proceed with the proof?

Homework Statement ||a|-|b||\leq{i don't know from here}\leq|a|-|b|\leq|a-b| Homework Equations n/a The Attempt at a Solution help

This is from a calculus textbook (self-study), but my problem is not with the calculus material itself. I feel I'm missing something (obvious!) from algebra. In any case: The problem statement Find an appropriate number L (a limit), and a deleted neighborhood N of a, such that a given e...

Homework Statement Suppose k>2, x, y in R^k, |x-y| = d > 0, and r > 0. Prove if 2r > d, there are infinitely many z in R^k such that |z-x| = |z-y| = r (In Principles of Mathematical Analysis, it is problem 16(a) on page 23.) Homework Equations |ax| = |a||x| |x-z| < or = |x-y| + |y-z|...

Can you help me solve this inequality for x? \frac{1+(\gamma+x(r-\alpha)-1)t}{1+\frac{\gamma+x(r-\alpha)-1}{2}}>0 where \gamma>1, 0<t<1, 0<r<3\alpha, \alpha>0 I really don't know where to start ...

Homework Statement Solve each sysytem usiing any method you wish: x2-y2=21 x+y=7 Homework Equations x2-y2=21 x+y=7 The Attempt at a Solution I chose to do the substitution method. so i change equation 2 to this: y=7-x and substitute it into the other equation in place...

I've been trying to wrap my head around the issues with Bell's Inequalities (while following the three related threads in this forum) and I think I finally have it figured out well enough to ask a question that's been bothering me. In particular, I'll start with...

I have no idea how to solve this inequality without using AM-GM inequality: for any positive integers p,q,x,y show that (pq+xy)(px+qy)>=4pqxy

Hey guys, I have some variables A,B, and C such that all must be greater then zero. A,B and C are all functions of K. I would like to find the range of values of K such that the 3 inequalities are satisfied. Is there a function built into Mathematica that will do this? I could write a...

I was considering complex numbers (independently) and I came across an interesting question. Are any of these statements true? 1<i 1>i i<-i -1<i -i<i<-1

Hello, I've got |a|^{2} = |a - b + b|^{2} What can I do with this guy? Usually when the square isn't there I use the triangle inequality and things fall out pretty quick, for example, |a| = |a - b + b| \leq |a-b| + |b| Is there something like that I can do with the orginial guy?

Homework Statement Find all numbers x for which x2+x+1 > 2 or x2+x-1>0 Homework Equations none The Attempt at a Solution essentially what I did is used the quadratic formula and I got x= \frac{-1\pm\sqrt{5}}{2} then I graphed the function and found that x2+x-1 > 0 when x <...

Homework Statement (1) Express the inequalities x≤3 and 1 ≤ x < 4 in interval notation.(2) Express in term of inequality: The distance between x and -3 is at least 5. The Attempt at a Solution (1) i don't know what he asking for ,,, can you explain it for me please (2) is it " x+(-3)≥5 "...

Homework Statement Let f:\mathcal{O}\subset\mathbb{R}^n\rightarrow\mathbb{R}, \mathcal{O} is an open convex set. Assume that D^2f(x) is positive semi-definite \forall x\in\mathcal{O}. Such f are said to be convex functions.Homework Equations Prove that f((1-t)a+tb)\leq...

Homework Statement let (X,\sigma) be a metric space. xyz \in Rshow that \mid \sigma(x,z)-\sigma(y,z) \mid \leq \sigma(x,y) Homework Equations The Attempt at a Solution \mid \sigma(x,z)-\sigma(y,z) \mid \leq \sigma(x,y)=\mid \sigma(x,y) \mid = \mid\sigma (z,x) +...

I am interested to know who to find upper bounds for derivatives of convolutions. If I know something of f and g, are there any major results about what kind of numbers C_{f,g} exist such that |D_x((f *g)(x))| \leq C_{f,g} ?

Alright let's just say (x-2)^2>12, find x can someone tell me what happens to the inequality sign when you take the square of the left hand side to the right hands side? does it swap?

Homework Statement Assume: 1) f(x) \rightarrow yo as x \rightarrow x0 2) g(y)\rightarrow l as y \rightarrow y0 3) g(y0) = l Prove that g(f(x)) \rightarrow l as x \rightarrow x0 Homework Equations Definition of function tending to limit - E is a subset of R, f:E->R, f tends to l...

Solve Inequalities with answers in Interval notation. x^2 + 1 > 4x Solve for x, U = Union x^2 - 4x + 1 > 0 x= 3.732050808, 0.2679491924 Answer x= 3.732050808 U 0.2679491924 ?

Homework Statement hy guys ,help me prove if x<y and n is odd ,then xn<yn i have solved this . .but a question in below Homework Equations The Attempt at a Solution if 0=or<x<y then xn<yn (i have proved this ) and if x<y<or=0 we can say 0=or<-y<-x it implies -yn<-xn...

Homework Statement Instructions: For the following inequalities, determine if 0 is a number in the solution set. 1) 3x \leq x+1 \leq x-1 2) x(2x-1) \leq x+7 Homework Equations The Attempt at a Solution 1) LS: 3x \leq x+1 3x-1 \leq x -1 \leq -3x -1/-2 \geq -2x/-2 1/2...

Homework Statement Hi all What is a ">" called in English, and likewise, what is ">=" called in English?

Hi all ! What chronology of Bell inequalities testing ( their violation ) ? What positive and negative aspects of each experiment ? What experiments have been spent latest years ? Some material: http://arxiv.org/PS_cache/quant-ph/pdf/0310/0310192v1.pdf Thanks.

If you have T < M + \epsilon, where \epsilon > 0 is arbitrary, does this imply T \leq M?

Homework Statement 1) x^5 > x^2 2) 7| x + 2 | + 5 > 4 3) 3 - | 2x + 4 | <= 1 Homework Equations The Attempt at a Solution 1) x5 - x2 > 0 x2(x3 - 1) > 0 x2(x - 1)(x2 + x + 1) > 0 Im not too sure what to do next. I can't factor it any further, at least I don't think so. Which...

Homework Statement I encountered a few problems while attending a problem solving seminar. Abstract mathematics and real analysis is not my forte and haven't really taken any courses in that regard. Thought maybe someone here could offer some help in better understanding about the following...

Homework Statement Here are two, unconnected example problems, having to do with quadratic inequalities. I'm confused b/c I understand how to solve them with an = sign, but as inequalities the book shows extra steps where signs get reversed and a total of ~ 4 possible answers come up instead...

So I need help with setting up the equation to graph it (eg. y = mx + b) but with different variables. In a factory, Machine A Produces 60 Cornflakes boxes per hour and Luckycharms at 70 boxes per hour. Machine B produces produces 40 cornflake boxes per hour and Luckycharms 40 per hour. It...

Homework Statement Prove that the set D = {z in C; |z^2 - 1| < 1} is open Homework Equations The Attempt at a Solution I have to show that for any z in D, there exists r > 0 s.t. the nbhd N(z,r) is contained in D. Let w in N(z,r) => |z - w| < r. Need to show |w^2 - 1| < 1 for some...

Homework Statement Solve the following equations or inequalities in the interval [0, 2pi) tanx - 3cotx = 0 Homework Equations The Attempt at a Solution tanx = 3cotx tanx = 3/tanx tan2x = 3 tanx = +-sqrt3 tanx = sqrt3 or tanx = -sqrt3 tanx = sqrt3 x = pi/3, 7pi/6...

Ok... So today, someone asked me a simple question: Why do two negatives become a positive number when multiplied together? This is intuitively basic, but not as easy to prove (unless there's some simple proof that I didn't think of). This was the basic proof that I came up with: Let a, b, c >...

Linear inequalities! I need help solving the following inequality: ABS value(7x-8) <=4x+7 +/-(7x-8) <=4x+7 7x-8 <=4x+7 -(7x-8) <=4x+7 7x-8-4x <=4x+7-4x -7x+8 <=4x+7 3x-8<=7 -7x+8-4x <=4x+7-4x...

Homework Statement |x+2/x+1|less than or equal to |x-3| how do i solve this?? I couldn't find any way! My lecturer did give me a hint saying that there are four combinations of + and -ve signs. Homework Equations The Attempt at a Solution

Homework Statement Prove: 2n + 1 < 2n , with n >= 3Homework Equations The Attempt at a Solution 2 (3) + 1 = 7 and 23 = 8. So 2 (3) + 1 < 23. Thus the inequality holds with n = 3: Suppose the inequality holds with n = k Then 2k+ 1 < 2k: So 2k + 1 + 2 < 2k + 2 2k + 3 < 2k + 2k 2k + 3 < 2(2k) 2...

Homework Statement Let X be a random variable; show that for a>1 and t>0, P(X>=(1/t)(ln(a)))<=(1/a)(Mx(t)) Homework Equations The Attempt at a Solution I know, from a previous problem, that, where X is a random variable and K is a constant, P(X>t)<=E(exp(kX))/(exp(kt))...

Hi guys, I'm currently on holiday and my exam starts right after holidays. I bought this book to do some exercise but they only provided answers without solutions. So i wonder if you guys could help me :) 1. If 3 + \sqrt{3} is a root of the equation 2x2 + 3ax + 3b = 0, where a and b are...

anyone recommend a good book on inequalities??

Homework Statement Derive the following inequality. Homework Equations x^{2}+xy+y^{2} \geq 0 The Attempt at a Solution I don't know how to get started. How do you derive inequalities? I'm not looking for the answer, just general tips.