Inequalities Definition and 329 Threads

Hello Everybody , First of all, I would like to apologize that this problem contains 3 parts to it (3 questions) but they all relate to each other. You must complete one part to move on to the next part. With that being said, I have 3-part problem that I could use some assistance with. 1a...

Though I don't have access to the original 1969 paper, I think the way the inequality is ussually derived is not correct since the argument goes as follows: $$-2≤ A(a,\lambda)[B(b,\lambda)-B(b',\lambda)]+A(a',\lambda)[B(b,\lambda)+B(b',\lambda)]≤2$$ the first mistake in this inequality is the...

I am under the impression that the following cannot be stated, a < b, if the a term is a complex number and the b term is either a natural number or a complex number, or any other type of number for that matter. Firstly am I correct? Secondly, if I am, does there exist a theorem of some sort...

what do you think are the inspirations or motivations that lead to inequality statements like am-gm, bernoullie's inequality, etc...? are they inspired by physics, engineering...? learning them for the first time made me wonder where they came from. thanks!

Homework Statement Solve the following. Express answers in set notation. -2(x-2)(x-4)(x+3)<0 Homework EquationsThe Attempt at a Solution I know my four intervals are x<-3 , -3<x<2 , 2<x<4 , x>4. I thought the answer would be x<-3 and 2<x<4 however the answers are opposite of what I thought...

Here is a basic inequality question for which I cannot understand the answer: If -1<a-b<10 ,and -3\le b\le1 then what inequality represents the range of values of a2? I plug-in -3 and 1 for b for boundaries and get -4<a<11. Since the boundary is for a2, the range would be 16<a2<121. But why...

1. Find the centroids of the solids formed by rotating completely about the x-axis the plane regions defined by the following inequalities: (a) y^2 < 9x, y>0, x<1 (b) xy<4, y>0, 1<x<2 2. I used the equation for solids of revolution: Integral from a to b of (x[f(x)]^2.dx) / Integral from a to b...

Homework Statement Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities: -2x+y+z <=4 x-2y+z<=1 2x+2y-z<=5 x>=1 y>=2 z>=3 Homework Equations I want to find the vector in the set with the maximal length. The Attempt at a Solution I have transformed the linear...

Homework Statement What is difference in shading between Argand diagrams containing inequalities with > and ≥ signs? Example Shade the appropriate region to satisfy the inequality |z|> 5 |z|≥ 5 The Attempt at a Solution I am aware of the fact that both will have circle centered at origin...

Homework Statement Find the set of all ##x## for which ##\dfrac{2x}{2x^2 + 5x + 2} > \dfrac{1}{x + 1}## Homework EquationsThe Attempt at a SolutionI'm getting two different sets of answers with two different methods:Method 1-Wrong ##\dfrac{2x}{2x^2 + 5x + 2} > \dfrac{1}{x + 1}####\dfrac{2x^2...

Hey everyone, I have a logic question, though I'm not sure if this might belong in the math forum (probably not :P) Anyway, I'm writing a BASIC compiler for the Motorola 68k processor by reverse engineering a dead project/compiler (with permission from the author as he's abandoned it years...

My goal is to master inequalities so that I can have a deep understanding of a book like the Cauchy -Schwartz Master Class by Steele. Right now, that book is too difficult for me. I want to work upto that level and have good intuition about inequalities. Are there any good books where I can hone...

Hello! What I'm wondering is if you want to prove an inequality, let's say ##a<b## and you already know that ##a>c## is true. If you are able to prove that ##c<b## is true, would that go on to imply that ##a<b## is true also? If this is correct, is it known as a theorem? Thank you!

I need to prove: (n+1)*(log(n+1)-log(n) > 1 for all n > 0. I have tried exponentiating it and I got ( (n+1)/n )^(n+1) < e. And from there I couldn't go any farther, but I do know that it is true by just looking at its graph. Could anybody help me please?

Homework Statement Prove that a.) (1-(1/n2))n > 1- 1/n b.) (1+ 1/(n-1))n-1 < (1 + 1/n)n when n=2,3,4,5,... Homework Equations [/B] Bernoulli's inequality (1+x)n ≥ 1+nx, when x ≥-1 and n=2,3,4,5,... (1+x)n >1+nx, when x ≥-1, x≠0 and n=2,3,4,5,..The Attempt at a Solution a.)[/B] I applied...

Homework Statement Arg z≤ -π /4 Homework EquationsThe Attempt at a Solution I'm confused whether the answer to that would be more than -45° or less. Should the approach to arguments be the same as in negative numbers?

Homework Statement The number of customers visiting a store during a day is a random variable with mean EX=100and variance Var(X)=225. Using Chebyshev's inequality, find an upper bound for having more than 120 or less than 80customers in a day. That is, find an upper bound on P(X≤80 or X≥120)...

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

Homework Statement [/B] I am trying to solve the simultaneous inequalities (1) and (2) shown in the following image. The solution is provided, but I'm not sure how they solved for it. [PLAIN]http:// Homework Equations N/A The Attempt at a Solution [/B] I tried to solve this set of...

There is a recent article (Optics July 2015) claiming violation of Bell inequalities for classical fields: "Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields" https://www.osapublishing.org/optica/abstract.cfm?URI=optica-2-7-611...

Homework Statement How does P(-1<Z<1) equal to 1-2P(Z>1)? (So you can find the values on the Normal Distribution Table) Homework EquationsThe Attempt at a Solution I tried P(-1+1<Z+1<1+1) but ended up with P(1<Z+1<2).

Homework Statement Sketch the solid whose spherical coordinates (ρ, φ, θ): 0≤ρ≤1, 0≤φ≤(pi/2) Homework EquationsThe Attempt at a Solution I was thinking that since ρ represented the distance from the point of the origin and φ represented the angle between the positive z-axis and the ray through...

I quoted these post from other thread. I don't want to distract discussion in other thread so I'm starting a new one about statements in these posts. Basically the question is if we can violate Bell inequalities by two separated but correlated systems that can be as non-classical as we like (as...

Hi, If f'(x) >= f'(y) can we say that f''(x) >= f''(y) also holds ? And if yes under which conditions ? Thanks

Homework Statement [/B] Identify the open intervals on which the function ##f(x) = 12x-x^3## is increasing or decreasing Homework Equations [/B] ##f(x)=12x-x^3## ##\frac {df}{dx} = 12-3x^2 = -3(x^2 - 4)## The Attempt at a Solution [/B] I'm reading out of two textbooks. One is a...

Lorentz transformation. Time separation between two events in system S and system S' is given by Lorentz transformations \Delta t'=\frac{\Delta t-\frac{u \Delta x}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}} If event 2 is caused by event 1 in system S then ##\Delta t=t_2-t_1##. But it is possible to choose...

Although he is primarily an astrophysicist, Dirac medal-winning Oxford Professor James Binney has taught a Quantum Physics course to second-year students at the university for years. A series of 27 of his lectures for the course is featured on the university's official website. Binney's take on...

Homework Statement [/B] this is the problem , if x and y are real positive numbers , I need to prove $$4x^4 + 4y^3 + 5x^2 + y + 1 \ge 12xy$$ Homework Equations [/B] $$x^2 + y^2 \ge 2xy$$ (Variation of AM GM Theorem) The Attempt at a Solution but $$x^2 + y^2 \ge 2xy $$, so $$6x^2 + 6y^2 \ge...

Homework Statement Show that if f is an entire function that satisfies |1000i + f(z)| ≥ 1000, for all z ∈ C, then f is constant. Homework Equations (Hint: Consider the function g(z) = 1000/1000i+f(z) , and apply Liouville’s Theorem.) The Attempt at a Solution Ok, so I assume that as f is...

3x+4y\le12 3x+y\ge3 y\ge-1 I understand the how to plot these on a graph, just not sure how to solve these inequalities! Do you have to solve for x or y?

Homework Statement 81^5>32^x Find the maximum value of x in order to satisfy the inequality. Homework Equations Inequalities, indices The Attempt at a Solution Try to make the bases on both sides of the inequality same.

Homework Statement The Attempt at a Solution -1 < (z-w) /(1-z*w) < 1 [/B] Hi can give clue. I am clueless

Hi! At university I have got a problem set with lots of inequalities. Unfortunately there are no explanations given how to do them. In Highschool we only did very easy inequalities. Therefore I am looking for a resource for inequalities. Especially for more difficult inequalities like $$ 1...

Homework Statement Given that the force of gravitation between Planet A (the one in the left side of the drawing), Fa=3000/da2 and the force of gravitation between Planet B and the rocket, Fb= 6000/ db2. Assuming that the three bodies involved is in stationary. What are the distances (ranges)...

I have the inequalities 2<x<6,\quad 1<y<5,\quad y-2\le2x, \quad-2y\ge8-4x I have to solve these and plot it in a graph and show the region where they satisfy. I understand you have to find the common area and shade it. How do you find the points to plot for 2<x<6\quad and\quad 1<y<5 I think I...

Solve the following inequality: 6e) $(x - 3)(x + 1) + (x - 3)(x + 2) \ge 0$ So, I created an interval table with the zeros x-3, x+1, x-3 and x+2 but I keep getting the wrong answer. Could someone help? (this is grade 12 math - so please don't be too complicated). Thanks.

1. if $|x-2|<A$, then $|2x-4|<3$ My steps: $$|2x-4|<3$$ $$2|x-2|<3$$ $$|x-2|<3/2$$ Hence, $A>3/2$, why does the answer say that $A\ge 3/2$? 2. if $|x-a|<5$, then $|2x-3|<A$ No idea how to do this one...I tried to manipulate the right inequality into a form such as $|2x-4|$, but I was...

1) True or Fale? |a-b| \geq ||a|-|b|| My solution: I broke this up into 4 different cases. 1. a> 0 b>0 2. a<0 b<0 and so on... For each case, I ended up with a more simplified version of the inequality. For instance, in case 1 where I used a<0 and b<0, I ended up with the simplified statement...

1.On the same axis sketch the graphs of y = (x-a)^-1 and y = 4|x-a| This part i have completed, the first equation has a horizontal asymptote at x = a, it being rectangular hyperbola. the second equation drawn too. 2. Solve (x-a)^-1 < 4|x-a|, giving your answers in a. Now the second part...

(This isn't homework, so I guess it'd go here...) Okay, so I'm trying to solve a system of equations with a bunch of ranges: (Some number between 1.2 and 2.0) = (Some number between 5.5y and 9.1y) = (Some number between 5.4x and 10x) Where X and Y are ranges made up of two percentages (or...

referring to the photo attached, can anyone expalin and give suitable numerical example please? i couldn't understand the notes.

So i have an equation to calculate the impossibility of pair production during photon decay into two electrons and I'm having to do some momentum conservation, can't quite do it but a colleague of mine has suggested this which I don't particularly agree with some help would be appreciated. So...

Homework Statement Show that if a>-1 and b>a+1 then the following integral is convergent: ∫(x^a)/(1+x^b) from 0 to ∞ The Attempt at a Solution x^-1 < x^a < x^a+1 < x^b x^-1/(1+x^b) < x^a/(1+x^b) < x^a+1/(1+x^b) < x^b/(1+x^b) I also know any integral of the form ∫1/x^p...

Lets suppose we have two inequalities, First inequality is x-y≤a-b≤x+y Second inequality is t-g≤c-d≤t+g How can I multiply these inequalities Thanks

Homework Statement 1/z - 1/2z - 1/5z = 10/(z+1) This is the equation presented right after in the textbook where the author explains how to use the LCD to convert this equation into a more understood linear equation. Homework Equations Here is the example before this equation...

Here is the question: I have posted a link there to this thread so the OP can view my work.

These are the two last problems I'll bother you with for a short while (I love this forum, I'll definitely stay on and hopefully be able to contribute in the future). Homework Statement Problem 1: (##-x^2##-1)sin2x > 0 , xe[0,2\pi] Problem 2: ##2^{-x^2+x+2}## < 4 Homework...

Note: I think I solved this while writing this topic, did not want to scrap it! if you think its wrong let me know! I am trying to manipulate the rectangular function with different arguments and came across a confusing one Trying to show: \prod (x^2) = \prod (\frac{x}{\sqrt{2}}) Recall that...

Hi everyone, let's stay I have two inequation set such as: First one is A:= X_1-X_2 \leq 1 X_1 \leq3 X_2 \geq 1 X_1,X_2 \geq 0 Second one is B:= X_1+X_2 \geq 5 X_1\leq5 X_1\geq4 X_2\leq4 X_1,X_2 \geq 0 I had like to write it as a set C := A\oplus B, with C made of linear inequations too. I'm...

I seem to be having trouble with multivariable epsilon-delta limit proofs. I don't have a very good intuition for how \epsilon relates to \delta. For example: Prove \lim_{(x,y) \to (0,0)}\frac{2xy^2}{x^2+y^2} = 0 There are probably many ways to do this, but my teacher does it a certain way...