Inequalities Definition and 329 Threads

Homework Statement A sequence (Xn) is defined by X1=3 and Xn+1= (6Xn+1)/(2Xn+5) for all n\in N. Prove by induction or otherwise that Xn-1 > 0 for all n \in N. Homework Equations The Attempt at a Solution I'm not sure with what to do when dealing with inequalities in an...

Homework Statement Determine whether a vector x exists that satisfies the above equation. Homework Equations This is not an actual HW problem, and it is not from a book. (There is no section before or after that explains or introduce this problem or problems similar to it.) So I...

What are linear inequalities actually used for?

Hi, can someone tell me when should i change my sign when i have such a problem? -(75/x) > 15 i find that if -75/x > 15 i could do : -75 > 15x -5 > x x < -5. or 75/-x > 15 i could do : 75 < -15x -5 > x which the answer in the book says -5 < x < 0 Thanks.

Trying to plot the set of complex numbers \{z \in C | |z - i| \leq |z-1|\} on the complex plane. I've tried by hand a few values for z, such as z = 1 - 2i, z = 2 + 2i, but the inequality isn't true. How can I determine which values of z are true for this inequality?

Homework Statement 3x+1 2x-4 > 0 The Attempt at a Solution My answer came to be (x< 1/3) U (x>2)

I wanted help on solving Solving Rational Inequalities. I watched this video and i was wondering if that was the best or easiest way. Our teacher taught us a much harder and weirder way using multiple number lines instead of one. If you do watch the video the man shows examples with open dots...

Homework Statement Find all real values of X | x - 1 | + | x + 1 | < 1 and | x - 1 | . | x + 2 | = 3Homework Equations The Attempt at a Solution some how i am thinking i should just solve em as is and all should be fine but i think I am lacking a lil bit of fundamental knowledge - some...

I never have much luck when something says "prove something <= something else". I usually just fiddle around and occasionally get lucky and reduce it to a constant < an express I know can't be less than that constant. But most times I can't reduce it to something like that. Is there any kind of...

Homework Statement With n>1, show that (a) \frac{1}{n}-ln\frac{n}{n-1}<0 and (b) \frac{1}{n}-ln\frac{n+1}{n}>0 Use these inequalities to show that the Euler-Mascheron constant (eq. 5.28 - page330) is finite. Homework Equations This is in the chapter on infinite series, in the section...

Question 1) {(u1,u2) : -∞ < (u1+u2)/2 < ∞ and -∞ < (u1-u2)/2 < ∞ } = {(u1,y2) : -∞ < u1 < ∞ and -∞ < u2 < ∞} Why is the equality(=) true? How can I see that the two sets describe the same region? Question 2) 2) Define u1=y1+y2, u2=y1-y2, so the mapping (or function) is...

Proving inequalities - Does induction work?? Homework Statement prove that, for a,b,c>0, a+b+c=1, 1/a+1/b+1/c≥9 Homework Equations it says that i might want to use the fact that for all X=/=0, X+1/X ≥ 2 The Attempt at a Solution using the tip I could make it: a+1/a+b+1/b+c+1/c ≥...

Homework Statement For real numbers x and y prove the following: llxl - lyll < (or equal to) lx - yl Homework Equations The Attempt at a Solution Im not really sure where to start, i was considering cases where x < 0 and say y< 0 and what that would imply say x-y would be...

Alright again I am having trouble with a few problems. I am unsure on the first two problem's answers and I have no idea how to do the third one..Solve and graph the solution on a number line 0 < |x + 3| < 1 I get: -3 < X < -2 or -3 > X > -4 and it graphs like this (is this right?)...

Homework Statement The Questions are 2x - 3 > x + 15 -4 x = 2 < 10 ( I am not sure how to place a line under the < on my computer) and -5x + 1 < -2x + 10 I have never done these type questions before and if anyone is really good at explaining the answers, I would greatly appreciate it so...

I'm taking an algebra & triginometry class at my college and my professor is kind of slow and unclear. I think I'm a fast learner and a good understander which is why I came here to get this info down. We're up to complex fractions or radical equations right now I think, forgot which. Something...

Homework Statement lxl <2 lx+2l The question is asking to solve this Homework Equations The Attempt at a Solution Ive tried bringint the 2 over which leads me to l-x-4l over lx +2l < 0 but then the absolute value confuses the heck out of me on where to go...

Homework Statement a,b,c are the sides of the triangle. then find the range of \frac {a^{2}+b^{2}+c^{2}}{ab+bc+ca} The Attempt at a Solution Let; \frac {a^{2}+b^{2}+c^{2}}{ab+bc+ca}=k cross multiplying and adding 2(ab+bc+ca) on both sides then; \frac{(a+b+c)^{2}}{ab+bc+ca}=k+2...

hey guys just checking if this is correct... -------------------------------------------------------------------------------- |x-2|(greater than and equal to) 4 = -2 (greater than and equal to) x (greater than and equal to) 6 is this correct? thanks u and 1 (less than or equal...

Homework Statement (cos(x))^p \leq cos(px) 0\leqx\leqpi half and p, 0\leq(not equal) p \leq(not equal) 1 i need help, if some one can tell me how to started, what should i used i will really apreciate it! (sorry for my english :confused:) Homework Equations The Attempt at...

Homework Statement Solve the following inequality and express the solution set in interval notation. http://www.webassign.net/www24/symImages/4/6/aaf987edafbf00c172f8cfaf01966c.gif The Attempt at a Solution I got most of the answer right, except the lower interval. the answer is...

An equality that is true for all members of a specified set is generally called an "identity" (for example x+x=2x is, say, an identity wrt the set of real numbers). But do inequalities that are true for all members of a specified set have an established name? (An inequality of that kind...

Problem: \frac{3}{|x+1|-1}+\frac{2}{x}<1 My Solution: There are 2 cases: 1) x\geq0,\frac{3}{x+1-1}+\frac{2}{x}<1 \frac{3}{x}+\frac{2}{x}<1 And you end up with... x>5. 2) x<0, \frac{3}{-x-1-1}+\frac{2}{x}<1 \frac{3x-2x-4}{-x^{2}-2x}<1 ... a few reductions later... x^{2}+3x-4>0 And...

Hello Guys, I'm new to these boards, just wanted to say hi before I start my post. I had some questions about solving equations and inequalities which I wasn't sure how to do... Find all solutions for \theta \in [0, 2\pi] (I) sin(\theta - \frac{\pi}{4}) = \frac{\sqrt{3}}{2} (II)...

http://img295.imageshack.us/img295/2538/q1qj1.th.jpg http://img410.imageshack.us/img410/307/a12ku8.th.jpg I am having trouble with the final part of this question - part f; I can do all the previous parts. I have attached the questions and markscheme, and so woulkd appreciate it if someone...

Homework Statement Find the solution set of: |x+1| + |x-2| \leq 5 Homework Equations I'm going to rearrange this to |x+1| \leq 5 - |x-2| The Attempt at a Solution Well i sketched a graph of it. The line 5-|x-2| cross the y-axis at 3 and it 'pongs' back of the x-axis at -3...

Hey, my stuff is done in LaTeX if you want to copy into a document and compile it. I guess if you can read TeX you can read it without resorting to that though. My TeX is not the neatest, if you have any problems please tell me. Homework Statement 1. Let $S$ be a nonempty set of real...

Hi all, I'm trying to teach myself analysis using the book "A Companion to Analysis: A Second First and First Second Course in Analysis" by T. W. Körner. There's an inequality problem in there that's used to prove a statement about the continuity of a function, that I've got stuck in...

I want to get a book on inequalities to help prepare for the Putnam exam. Its common for me to spend about half an hour getting frustrated on a practice problem and then find that the only way to do the problem is with an inequality that I have never heard of. Does anyone have any...

Hi, Is there a polynomial time algorithm (polynomial time in terms of the number of input constraints and variables) to solve a system of linear inequalities or or indicate whether a solution for a system of linear inequalities exists or not? Thanks

Homework Statement Find the values for x. 3sin^2x - 3sinxcosx + 2cos^2x > 1 Homework Equations The Attempt at a Solution 3sin^2x - 3sinxcosx + 2cos^2x > 1 3sin^2x - 3sinxcosx + 2cos^2x > sin^2x+cos^2x 2sin^2x - 3sinxcosx + cos^2x > 0 What to do next?

According to some models of inflationary cosmology, the multitude of universes in the multiverse are connected by tiny wormholes that pop in and out of existence in the quantum foam. These wormholes can supposedly be formed in particle collisions. Could negative energy be used to hold these...

show that 1/2+1/3+...1/n < \int dx/x < 1+1/2+1/3+...1/(n-1) inside the integral is from 1 to n. thx

Interesting short article: http://www.slate.com/id/2161309/

Hey..This is a question I am having difficulty in solving. 4x\angle2x+1\leq3x+2 First I removed the "1"from the centre. Then I tried eliminating the X's from both sides, but that did not work. Could someone help me with this?

Give the interval notation for the inequality: \displaystyle{x\leq -2 My answer is: \displaystyle{(-\infty, -2]} Book answer is: \displaystyle{(\infty, -2]} ?

x+|x|=y+|y| so for x which in a sense will be the same for y x if x > 0 -x if x < 0 now does that only apply to my absolute x? or does it apply to both x and |x|?

Homework Statement Prove ln(1+x)>=(x)/Sqrt(1+x) Prove (x-1)^2>=x((ln(x))^2) For x>0 Homework Equations The Attempt at a Solution I have tried using MVT, but i only end up with more inequalities that i cannot seem to prove... Another idea that works but i cannot prove exactly...

Homework Statement Mnimize and maximize: P=30x + 10y Subject to 2x + 2y > or = 4 6x + 4y < or = 36 2x + y < or = 10 x, y > or = 0 Homework Equations The Attempt at a Solution How would I go about graphing this on my calculator: 2x + 2y > or = 4...

[SOLVED] Quadratic Equations and Inequalities question about properties of quadratic so here is the question graph the function. state the domain and range of the function. F(x)=-2x^2-3x+2 i try and use the axis of symmetry (-b/2a) and then plug that into the original formula to get the...

Homework Statement can someone help me with only if part of Problem 2? http://www.math.cornell.edu/~putnam/ineqs.pdf I can prove that quantity is less than or equal to n, but I cannot get it leq to 1? Homework Equations The Attempt at a Solution

A rectangular solid is to be constructed with a special kind of wire along all the edges. The length of the base is to be twice the width of the base. The height of the rectangular solid is such that the total amount of wire used (for the whole figure) is 40 cm. Find the range of possible...

Homework Statement Three functions are defined as follows: f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180 g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90 h:x>tan x for the domain p< (or equal to) x < (or equal to) q Find the range of f. -1<(or...

Argh, I haven't done any calculus since gr. 12 and university calculus is killing me. Need some help with a few questions; and I know there are a few that I'm asking for on here, but they are only a few out of many (I've done most). Homework Statement 1. Solve the following inequality. (graph...

\frac 1{3x^2-x-2}<0 I understand that in algebra inequalities, one side has to be made zero but in the equation shown above, I am unable to find the set of values that satisfies the equation.

stupid error in the "tex" thing, see first post.

hi, I've recently started looking into maths outside of class and am mostly interested in proof. however, when reading into it a bit i got confused as to what the book meant by a true proof, and a non-proof, and i would like you to clear a few things up for me if you can :D thnx. this is...

Hi, I am curious to kow about this smoothing concept that I've seen mentioned somewhere but do not understand. It would be great if someone could explain it to me, preferably through a solution to this problem. Thanks for any comments. (Latex did not generate in the preview, so if it seems there...

ok so i missed a few classes and i have a test comming up soo and i need some help understanding inequalities. the example I am trying to do is: If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7 form what i could understand from a textbook was something like: -2<x-2<2 0 < x < 4 and...

Here is the question from the book: ------ Let n\geq1 and let a_1,...,a_n and b_1,...,b_n be real numbers. Verify the identity: \left(\sum_{i=1}^n{a_ib_i}\right)^2 + \frac{1}{2}\sum_{i=1}^n{\sum_{j=1}^n{\left(a_ib_j-a_jb_i\right)^2}} =...