Bounds Definition and 182 Threads

In sports, out of bounds (or out-of-bounds) refers to being outside the playing boundaries of the field. Due to the chaotic nature of play, it is normal in many sports for players and/or the ball to go out of bounds frequently during a game. The legality of going out of bounds (intentionally or not), and the ease of prevention, vary by sport. In some cases, players may intentionally go or send the ball out of bounds when it is to their advantage.

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  1. H

    What are the frequency bounds of waves from sine wave additive synthesis?

    Hello, If I can make any number of waves (n) all with the same phase but all within a frequency range of 100-200hz, what are the ranges of frequencies I can make when adding them? So would I be able to make a wave with frequency 400hz, or 25hz, using additive synthesis and these constraints...
  2. B

    Selecting the correct bounds for polar integrals

    Hi! Here's a question I am working on: Double integral of arctan(y/x). where R: 1≤x2+y2≤4, 0≤y≤x. I have the bounds for r as 1 to 2, but for θ I don't know if I should use ∏/4 to ∏/2 or 0 to ∏/2. How do I know which one? The integration is easy, but I need help with the bounds...
  3. A

    Derivative increasing without bounds

    if f'(x) > 0 for all real values of x then x increases without bounds. I thought that was true but in the back of the book it says false and uses f(x)=2x/sqrt(x2+2) as an example. i worked out the derivative and got f'(x) = 4/(x2+2)3/2. how does that show that the first sentence is false? I'm...
  4. G

    Calculus II - Taylor Series - Error Bounds

    Homework Statement Hi, I'm really struggling with trying to come up with the error bound when doing taylor series problems Use the reaminder term to estimate the absolute error in approximating the following quantitites with the nth-order Taylor Polynomial cnetered at 0. Estimates are...
  5. J

    Bounds of a band pass filter for image processing

    Hi all, I'm working on some image analysis as a part of my research, specifically trying to match images. The method I am using transforms the image into the frequency domain and then applies a band pass (or mesa) filter to eliminate noise and the dc component of the image. I have never...
  6. F

    Marginal PDF Bounds: Calculating Integration Limits

    Hey guys, So I'm having trouble telling what the integration bounds should be when calculation the marginal PDF of two random variables. So the joint PDF fX1,X2(x1,x2) is a constant C = 1 in the regions x1 and x2. The regions are bound by 0<=x1<=1 and 0<=x2<=2(1-x1). If the marginal PDFs are...
  7. P

    What are the bounds for evaluating a triple integral in the first octant?

    Homework Statement evaluate triple integral of z.dV where the solid E is bounded by the cylinder y2+z2=9 and the planes x=0 and y=3x and z=0 in the first octant Homework Equations for cylindrical polar co-ords, x=rcos\theta, y=rsin\theta and z=z The Attempt at a Solution im just...
  8. F

    Plus or minus in integrals? And figuring out new bounds

    Homework Statement Evaluate this integral using trigonometric substitution. \int_{0}^{2} \frac{x^3}{\sqrt{4-x^2}}dx Now I can do this the "textbook memorization" method like every calculus student does, but I want to go ahead an analyze this further. But I will show you the...
  9. L

    Finding the bounds of a triple integral in cylindrical coordinates?

    Homework Statement I took a picture of the problem so it would be easier to understand. All I need to know is what the bounds are. Homework Equations In cylindrical: x=rcos(theta) y=rsin(theta) z=z The Attempt at a Solution I don't know why we should change this to...
  10. R

    Confusion about the constant of integration and bounds

    When we integrate a derivative: What are the bounds? Shouldn't we then have this if the bounds are x2 and x1: but instead we have this:
  11. R

    MATLAB Index Out of Bounds Error - Troubleshooting in MATLAB

    I'm working on a piece of code to help me generate plots. Right now I'm focusing on the calculation stuff. Here's what I need to do. For each RPMline, calculate the Mach number (M0) for mdotf=.1,.2,.3,.4,.5,.6,.7 I read values of Tt4_Tt2_ratio, pi_c, eff_c, mdotcorr2 from the Excel sheet...
  12. V

    Integration bounds in a continuous charge distribution of a semicircle

    Why are the integration bounds from -pi/2 to pi/2 and not 0 to pi?
  13. B

    Bounds for non-linear recursive sequence

    Homework Statement We are given the real sequence x_n+1 = (x_n)^2 - 100 + sin(n), some x_0 Prove that if the sequence is bounded with positive numbers, then necessarily 10 <= x_n <= 11 for all n>=0. Homework Equations The Attempt at a Solution I tried induction and...
  14. R

    The Tetraktysal Kissing Triangle (TK_n) & Lower Bounds of Kissing Numbers to D=10

    The "Tetraktysal Kissing Triangle" (TK_n) & Lower Bounds of Kissing Numbers to D=10 The Tetraktysal Kissing Triangle (TK_n) Nickname: "The TetraKiss Triangle" A Fibonacci, Lucas, Tetrahedral Convolution Construction for Lower Bounds of Sphere Packings to Dimension 10 Based Upon the Pythagorean...
  15. L

    Optimizing Paraboloid Bounds for Triple Integral

    Homework Statement Evaluate the triple integral xdV where E is the solid bounded by the paraboloid x= 2y^2 + 2z^2 and x=2. The Attempt at a Solution The bounds I got are for z -sqrt(1-y^2) <= y <= sqrt(1-y^2) for y -1 <= y <= 1 for x 2y^2 + 2z^2 <= x <= 2 are these...
  16. L

    Finding bounds of triple integral

    Homework Statement Evaluate the triple integral of the function (x+5y)dV Where E is bounded by a parabolic cylinder and the planes z=9x z=0 y=18x and y=3x^2 I just wanted to knw if my bounds are correct. Here they are for dz: 0 to 9x dy: 18x to 3x^2 dx: 0 to 6
  17. A

    Dont understand the bounds of this integral, shell method.

    Homework Statement Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y=4x-x^{2} , y=4 , x=0 Homework Equations V=2\pi\int p(x)h(x) from a to b The Attempt at a Solution...
  18. P

    Determining bounds of a function

    Homework Statement decide if f is bounded above or below, and if f takes on maximum or minimum value f(x)= x^2 for x< or =a, a+2 for x>a on (-a-1, a+1), assuming a>-1 Homework Equations x^2 is continuous on R The Attempt at a Solution I have no idea where to start with this. I...
  19. S

    Can Lower Bound of Summation Be Any Real Number?

    can the lower bound of a summation(sigma) be any real number ? i.e ex: sigma(LB:sqrt(2) or (9/2) etc ) Even a lower bound be a real number is possible or not can upper bound be any real number or is it a strict rule that '1' should be added to lower bound to get the consecutive number.? i.e...
  20. Z

    Question About Spivak Proof Of Bounds

    Homework Statement Let A and B be two nonempty sets of numbers which are bounded above, and let A+B denote the set of all numbers x+y with x in A and y in B. Prove that sup(A+B) = sup(A) + sup(B). Hint: The inequality sup(A+B) <= sup(A) + sup(B) is easy. To prove that sup(A) + sup(B)<=...
  21. S

    Epsilon Delta Proofs, finding bounds

    Homework Statement Prove that lim x->3 of (x^{2}+x-5=7Homework Equations 0<x-c<\delta and |f(x)-L|<\epsilonThe Attempt at a Solution The preliminary analysis. The first equation in the relevant equations becomes 0<x-3<\delta And the second equation becomes |(x^{2}+x-5)-7|<\epsilon...
  22. W

    What evidence do we have for the existence of electron clouds?

    Hello. I have recently been introduced to the concept of electrons as standing waves around the atomic nucleus. The explanation I read used the simulation of "a particle in a tube" to give a monodimensional interpretation of how the standing wave behaves. Within an atom, what serves as the...
  23. P

    What are the Correct Bounds for a Triple Integral with Symmetry?

    I'm trying to set up this triple integral with the following bounds: x=0, y=0, z=0, x+y=1, z=x+y. Now I first computed the volume to be 1/3 with a double integral and then what I've been doing is setting what I think are the right bounds for the triple integral and integrating f(x,y,z)=1...
  24. S

    Bounds for the mean of the minimum of binomial random variables

    Dear Friends, I want to find an upper and lower bound for the expected value of the minimum of independent binomial random variables. What paper/book do you suggest for this problem? In other words, I need to find bounds for E(min(X1,X2,...,Xn)), where Xi 's are independent random variables...
  25. H

    Does the Maximum Principle Apply to Harmonic Functions in Bounded Regions?

    Homework Statement Let u(x; y) be real, nonconstant, and continuous in a closed bounded region R. Let u(x; y) be harmonic in the interior of R. Prove that the maximum and minimum value of u(x; y) in this region occurs on the boundary. Homework Equations the theorem said that( a...
  26. C

    What is the definite integral of 1/(36+x^2) with bounds [0, 6]

    Homework Statement What is the definite integral of 1/(36+x^2) with bounds [0, 6]? I've only been taught U substitution to handle problems like these. I let u = 36+x^2 and du=2xdx but I am stuck and don't know what to do. Te answer is pi/24 but I don't know how to obtain it. Is there a...
  27. M

    MATLAB Why Does My Matlab Code Give an Out of Bounds Error?

    Hey, I have defined pu = zeros(nx,ny,N); pv = zeros(nx,ny,N); pu(:,ny,:) = 1; and written the loop: line 38-40 for i = 2:(nx-1); for i = 2:(ny-1); ps(i,j) = p(i,j,n) - a1*(pu(i+1,j,n) - pu(i,j,n)) -a2*(pv(i,j+1,n) - pv(i,j,n)); and I get the error Could someone help me...
  28. M

    Help with finding least upper bounds and greatest lower bounds?

    Homework Statement Solve the following inequalities and express the solution(s) in interval notation and set builder notation. For each of these, state the least upper bound and greatest lower bounds, if these exist. Homework Equations i) x^3 + x^2 > 2x ii) l 2 - x l =< 4...
  29. I

    Proving Bounds on |1+x| when |x-1|<d

    Homework Statement Show the following for every d>0: For every real number x with |x-1|<d it follows that |1+x|<2+d 2. The attempt at a solution If x-1>0, then |x-1|=x-1<d. Hence x+2 = |x+2| < 2+d. If x-1<0, then |x-1|=-(x-1)<d. Hence x-1>-d => x+1 > 2-d ...?? Is this really possible to do...
  30. P

    What are the Bounds for the Region Bounded by Parabolic Cylinders and Planes?

    1. I need to find the region E bounded by the parabolic cylinders y=x^2, x=y^2 and the planes z=0 and z=x+y 2. y=x^2, x=y^2, z=0, z=x+y 3. I figured that I should let z vary between zero and x+y and then find x and y in terms of actual numbers? I'm not entirely sure. I've graphed it in...
  31. D

    Proving "Bounds of log(n)" Inequality

    Homework Statement Prove that for any integer n >= 2, 1/2 + 1/3 + ... + 1/n <= log(n) <= 1 + 1/2 + 1/3 + ... + 1/(n-1) Homework Equations None The Attempt at a Solution I can see pictorally why the inequality holds true but despite numerous am struggling to make any real...
  32. A

    Proving Existence of Zero with Least Upper Bounds

    Homework Statement sup problem if f is continuous on [a,b] with f(a)<0<f(b), show that there is a largest x in [a,b] with f(x)=0Homework Equationsi think it can be done by least upper bounds, but i dun know wat is the exact prove. The Attempt at a Solution
  33. D

    How Does Scaling a Set Affect Its Bounds?

    Homework Statement Let A contained in R be a set of real numbers. For c in R define set cA as cA: {x in R|x=ca for some a in A} a. prove that if c is greater than or equal to zero, then cA is bounded above and sup(cA)=cSup(A). b. prove that if c is less than zero, then cA is bounded...
  34. D

    MATLAB Troubleshooting MATLAB Index Out of Bounds Error: Tips and Solutions

    Dear forummers, I'm trying to solve a problem that is displayed in MATLAB below:- ? Attempted to access x(2); index out of bounds because numel(x)=1. Error in ==> fit_fun at 5 Fit_fun_val= x(1)^2 + x(2)^2 + x(3)^2; Error in ==> jack_immune at 47...
  35. jinksys

    Finding the Bounds of Theta for a Double Integral

    Example: Use a double integral to find the area of the region: One loop of the rose r = Cos[3 theta] Finding the bounds of r is easy, 0 to Cos[3x]. However, I usually get the bounds of theta wrong. How do I find the bounds of theta without using a graphing calculator and guessing. The...
  36. R

    Upper/Lower Bounds Homework: Solving (a), (b), (c)

    Homework Statement Let S=P{2,3,4,6,7,8,14,28,42,98} and let p be the relation on S defined by a p b iff a|b. Then (S,p) is a poset. (a) Find a subset of S which has no upper bound and no lower bound. (b) Find the least upper bound for {3,7} (c) Determine wether or not the subset {2,6,8}...
  37. W

    Finding Bounds for a Triple Integral

    Homework Statement Find \int \int \int_{D} xydV, where D is the solid bounded by the coordinate planes, the plane x = 1 and the surface z = 16 - 4x^2 - y^2. Homework Equations The Attempt at a Solution I have no problem with actually performing the integration, but I'm lost on...
  38. Y

    Changing bounds of integration of a double integral

    Picture of the problem is listed above. I'm not sure how to switch the bounds of integration on it. Anyone here know how to go about this? i tried doing it x^2 to 1 for y and then 0 to 1 for x but it didnt work out to be the write answer, the write answer after putting it in your calculator...
  39. W

    Center of Mass of a Triangle: Struggling to Find the Bounds

    Homework Statement Find the center of mass of the triangle with vertices at (0,0), (6,6) and (-6,6) if the density at (x,y) is equal to y. Homework Equations The Attempt at a Solution I am having trouble with these centroid/center of mass problems, and I can't even figure out the...
  40. B

    How Can We Estimate Bounds on the Sum of Distributions?

    Take any distribution function F(x) where the n-fold convolution F_n(x) is unknown or difficult to calculate. Here F_{k+1}(x) = \int_{-\infty}^{\infty}F_k(x-t)dF(t). Are there any good techniques for estimating bounds on F_n(x), given F(x) ? Suppose the distribution does not have...
  41. G

    Learn Chernoff Bounds: Step-by-Step Instructions & Examples

    Was wondering if anyone had a good source on Chernoff Bounds? Looking for something that is easy to follow and has good step by step instructions and/or a good example. Thanks, space
  42. H

    Understanding the Principles of Hashin-Shtrikman Bounds: A Simple Explanation

    Is anyone familiar with the Hashin-Shtrikman bounds and the principles behind them? Will you be so kind as to post a simple explanation? So far, what I have grasped is that they came up with a functional and the bounds are obtained when a certain tensor is chosen to be positive...
  43. marcus

    Tighter bounds on cosmo parameters (Chandra Cluster Cosmology Project)

    http://arxiv.org/abs/0812.2720 Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints A.Vikhlinin, A.V.Kravtsov, R.A.Burenin, H.Ebeling, W.R.Forman, A.Hornstrup, C.Jones, S.S.Murray, D.Nagai, H.Quintana, A.Voevodkin ApJ, in press: Feb 10, 2009 issue (Submitted on 15 Dec...
  44. C

    Double integral bounds after polar transformation

    Homework Statement Basically I'm just trying to convert a double integral into polar coordinates, but when I do it I get confused with my bounds. Homework Equations The Attempt at a Solution 4\int_0^{\infty}\int_0^{\infty}e^{-(u^2+v^2)}u^{2x-1}v^{2y-1}dudv (x and y are just numbers, not...
  45. T

    How to find the bounds of this siquence

    (n^2+2)^0.5 - (n)^0.5 i thought of doing a limit where n->infinity but here i get undefined form and even if i whould get some finite limite it will only be one bound and i can't do limit n->-infinity because its a sequence must be positive??
  46. 3

    Is Uniform Continuity a Property of Bounded Functions?

    Homework Statement Show that if a function f:(0,1) --> lR is uniformly continuous, f is bounded. Homework Equations - The Attempt at a Solution Really don´t know. I started thinking about Weierstrass Thereom but I am not sure that it´s ok. Now I think that may be is something...
  47. Saladsamurai

    Triple Integral: Having trouble finding my y bounds

    Homework Statement I=\int\int\int_E x^2e^ydV where E is bounded by the parabolic cylinder z=1-y^2 and the planes z=0 x=1 and x=-1 I know that the graph is a parabola that opens downwards and that has symmetry wrt the x-axis. It also stretches along the x-axis toward + and - infinity...
  48. B

    Triple integral finding bounds?

    Homework Statement Integrate the function over the solid given by the figure below (the bounding shapes are planes perpendicular to the x-y plane, a cone centered about the positive z-axis with vertex at the origin, and a sphere centered at the origin), if P=(0,0,5),Q=(0,4,3), and...
  49. B

    Finding bounds on triple integral?

    Homework Statement Integrate the function over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and and contained in a sphere centered at the origin with radius 20 and a cone opening upwards from the origin with top radius 16...
  50. J

    Exercise on Posets, Chains and upper bounds

    Homework Statement Suppose X and Y are sets. Let P be all pairs (A,f) where A is a subset of X and f is a function from X to Y. Then P is a poset with the relation (A,f)=<(B,g) iff A is a subset of B and f is the restriction of g to A. Show that if C={(Ai,fi)|i in I} is a chain in P, there is...
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