What is Bounds: Definition and 182 Discussions

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. Confused about polar integrals and setting up bounds

So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds. Any help would be greatly appreciated! Thanks!!
2. A Range of Difference: Bounds for Length of Stay

Ok, so I'm given hotel data :{Arrival Date, Departure Date}, each in terms of nth day of the year , and I want to estimate whether the range/difference, aka, the length of stay is below a bound. Say a week ( 7 days) for definiteness. I'm thinking of using either the distribution of the range...
3. Electric Field as a function of r, evaluating bounds

Im having trouble understanding the wording to this problem. When it says "from r=0 to r=infinity". My Qenc would zero out. I guess it makes sense that from infinitely far away you wouldn't "feel' the electric field but considering this question leads to 4 other questions I don't think I am...
4. I Error bounds for Newton's Method

Hi, PF Sometimes it is not easy to find roots of functions. Newton gave a nice clue: the Newton's Method formula: ##x_{n+1}=x_n-\dfrac{f(x_n}{f'(x_n)}##. My concern is, now that I have understood and practiced it, comprehend what I've sketched in the summary. This is all taken from "Calculus...
5. MHB Upper and lower bounds for the cardinalities

Hey! :giggle: Let two relations $M$ and $N$ be given with the cardinalities $m$ and $n$ respectively. Determine and justify the upper and lower bounds for the cardinalities of the following relations: - $M\cup N$ : - $M\times N$ : - $M\cap N$ : - $M\setminus N$ : - $M\Join N$ : -...
6. Bounds of the remainder of a Taylor series

I have found the Taylor series up to 4th derivative: $$f(x)=\frac{1}{2}-\frac{1}{4}(x-1)+\frac{1}{8}(x-1)^2-\frac{1}{16}(x-1)^3+\frac{1}{32}(x-1)^4$$ Using Taylor Inequality: ##a=1, d=2## and ##f^{4} (x)=\frac{24}{(1+x)^5}## I need to find M that satisfies ##|f^4 (x)| \leq M## From ##|x-1|...
7. Please evaluate this double integral over rectangular bounds

Summary:: Could someone please evaluate this double integral over rectangular bounds? Answer only is just fine. [Mentor Note -- thread moved from the technical math forums, so no Homework template is shown] Hi, I'm trying to find the answer to the following integral over the rectangle...
8. Find the bounds after changing the variables in a double integral

The answer calculates the integral with ##du## before ##dv## as shown below. However I decided to compute it in the opposite order with different bounds. Here is my work: According to the definitions, $$\begin{cases} u=x+y\\ v=2x-3y \end{cases}$$ First we need to convert the boundaries in xy...
9. I Connecting wave equation with a non-constant force only in bounds

Hi hi, I'm confused about how to mix this two concepts, actually the wave equation: ##\frac {\partial^2 u} {\partial t^2} = v_x^2 \frac {\partial^2 u} {\partial x^2} + v_y^2\frac {\partial^2 u} {\partial y^2} + force## The equation will apply the rule all over the space, but I have the next...

15. Comp Sci Java - Why no out of bounds error for this array

I am writing a class called "Course" in Java so that one can input students names, etc. Here is my relevant code for the Course class: public class Course { private String courseName; private String[] students = new String[0]; private int numberOfStudents = 0; public...
16. Double integral - What are the upper and lower bounds?

Cant get my head around the order of the upper and lower bounds for this, Is it always the higher take away the lower?
17. B Long term sustainable energy bounds

Is there an upper bound on the amount of sustainable energy/unit time that could ever be made useful to mankind? For instance, if we imagine that the entire surface area of the Earth were covered with deserts and no cloud ever appeared in the sky and then computed the rate of sunlight energy...
18. Prime Factors Bounds in a Recurrence

Let $$g(n)$$ be the numerators of the elements of the recursion $$i(n)=i(n-1)+\frac{1}{i(n-1)}$$ when they are expressed in simplest form, with $$i(0)=1$$. Let $$p$$ be the smallest prime factor of $$g(m)$$. Show that $$p>4m-4$$.Homework Equations Euler's Theorem? The Attempt at a Solution OEIS...
19. B Bounds for the index of a radical

Hi, I know that, at least formally, the index of a radical should be positive and integer. That is if I introduce \sqrt[x]{2} I need to assume x\in \mathbb N and x>0. However, my calculator has no problem in calculating the radical for any x\neq 0, say x=-\pi. The result it gives is based on...
20. MHB Bounds of the difference of a bounded band-limited function

for continues signal (function) we have Bernstein inequality : $$|{df(t)}/dt| \le 2AB\pi$$ where A=sup$|f(t)|$ and B is Bandwidth f(t), the question is:Is there a relationship for discrete function x[n] like this? $$|x[n] -x[n-1] | \le\ \mu\ W$$ where  X[k] = \sum\limits_{k =...
21. Expected bounds of a continuous bi-variate distribution

Homework Statement [/B] ##-1\leq\alpha\leq 1## ##f(y_1,y_2)=[1-\alpha\{(1-2e^{-y_1})(1-2e^{-y_2})\}]e^{-y_1-y_2}, 0\leq y_1, 0\leq y_2## and ##0## otherwise. Find ##V(Y_1-Y_2)##. Within what limits would you expect ##Y_1-Y_2## to fall? Homework Equations N/A The Attempt at a Solution...
22. Set of least upper bounds multiplied by a constant

Homework Statement Let ##S,T \subseteq \mathbb{F}## be nonempty sets. Assume ##\sup (S)## and ##\sup (T)## both exist in ##\mathbb{F}##. Show that ##\forall a \in \mathbb{F}^+ \cup \{0\}## we have ##\sup(aS) = a \cdot \sup (S)##. Homework EquationsThe Attempt at a Solution First I prove the...
23. A Unpacking Entropy Bounds and Their Violations

There is something that is unclear to me, and because entropy bounds and their violations were discussed in the other thread, I thought it is a good opportunity to learn something. The problem is essentially a matter of impression. The statements go roughly in the following way: for a system...
24. B Upper and Lower Bounds of Polynomials

Say we have a polynomial ##f(x)=2x^3+3x^2-14x-21## and we want to find the upper and lower bounds of the real zeros of this polynomial. If no real zero of ##f## is greater than b, then b is considered to be the upper bound of ##f##. And if no real zero of ##f## is less than a, then a is...
25. Bounds Integral of x times arcsine

Homework Statement Prove the integral of x*arcsine(x) from 1/2 to 1 is bounded between pi/16 and 3*pi/16 Homework EquationsThe Attempt at a Solution Not sure what to bound with. Do we use Squeeze Theorem?
26. I Normalization of integral bounds

Say we have a difficult integral of the form ##\displaystyle \int_a^{b}f(x) ~dx##. Let ##t = \frac{x-a}{b-x}##. Then ##\displaystyle \int_0^{\infty}f \left( \frac{bt+a}{t+1} \right)\frac{1-a}{(t+1)^2} ~dt##. My idea is that making this change of variables transforms the integral into a form...
27. Finding Volume of Solid Bounded by Paraboloid and Planes

Homework Statement Find the volume of the solid enclosed by the paraboloid z=x^2 + 3y^2 and the planes x=0, y=x, y=1, z=0 Homework Equations I'm not really sure what's getting me about this, but I'm not really sure how to proceed after finding the x, y, and z intercepts... The Attempt at a...
28. B Integration Bounds for E-field Calcualtion

Hi guys. I’m looking at the brute force way at getting the E-field for a uniformly spherical charge distribution. The location of the E-field of interest is anywhere outside of the sphere. Here are some images Everything makes sense. I’m just not sure why the bounds for ‘s’ where z-r to...
29. Help with bounds for integration

Homework Statement I'm trying to change the bounds for this integral Sin(x^2)dxdy With x going from 1 to 2y, y going from 0 to 1 (I already know the integration for sin(x^2) The Attempt at a Solution I converted 2y=x to 1/2x=y and graphed all the bounds. I went with 1,2 for my...
30. Proofing Bounds of Natural Numbers Set in Math: Is it Clear?

Homework Statement Consider the sets below. For each one, decide whether the set is bounded above. If it is, give the supremum in ##\mathbb{R}##. Then decide whether or not the set is bounded below. If it is, give the infimum. Finally, decide whether or not the supremum is a maximum, and...
31. Upper & Lower Bounds Real Zeros-Polynomial Division, Proofs?

Homework Statement Upper Bound[/B] If all of the numbers in the final line of the synthetic division tableau are non-positive, prove for ##f(b)<0##, no real number ##b > c## can be a zero of ##f## Lower Bound To prove the lower bound part of the theorem, note that a lower bound for the...
32. Marginal pdf, what am I doing wrong?

Homework Statement f(xy)=49/8*e^(−3.5*y) 0 < y < inf and −y < x < y 0 otherwise a. Find the marginal probability density function of X, fX(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for...
33. I Upper and lower bounds of integral

Is it always true that: Noticing that it works for some functions, I wanted to ensure it is true for all of them( at least polynomical), but since I am still in high school, and I don't have deep understanding in calculus( yet), the question is forwarded to you. proof please!
34. A What are the bounds of a ratio with a given set of numbers and variables?

Sorry in advance if I've posted in the wrong section. given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}## where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##How would you go about finding the bounds of something like this, or determining if it even has any? ##( \...
35. Multivariable integral with unclear bounds

Homework Statement Hi everybody! I'm trying to solve the following problem and I am unsure about what I did: Calculate ##\int_M f(x,y) dx dy## with ##M = \{ (x,y) \in \mathbb{R}^2: x^2 + y^2 \leq 1, x \geq 0, y \geq 0 \}## and ##f(x,y) = xy^2##. Homework Equations One equation I'd like to...
36. I Bounds on Chebyshev Function ##\theta (x)##

Hello, I remember reading somewhere that Dusart proved that ##\theta (x)<x## for very large ##x##. Where ##\theta (x)## is the first Chebyshev function (the sum of the logarithms of all primes less than or equal to ##x##). I couldn't find any source for this and was wondering if anybody had...
37. Upper and lower bounds of a triple integral

Homework Statement Let ##T \subset R^3## be a set delimited by the coordinate planes and the surfaces ##y = \sqrt{x}## and ##z = 1-y## in the first octant. Write the intgeral \iiint_T f(x,y,z)dV as iterated integrals in at least 3 different ways. Homework Equations \iiint_T f(x,y,z)dV =...
38. Differentiability of a function -- question on bounding

Homework Statement I need to see if the function defined as##f(x,y) = \left\{ \begin{array}{lr} \frac{xy^2}{x^2 + y^2} & (x,y)\neq{}(0,0)\\ 0 & (x,y)=(0,0) \end{array} \right.## is differentiable at (0,0) Homework Equations [/B] A function is differentiable at a...
39. Regarding Schwartz inequality and integration bounds

Based on Schwartz inequality, I am trying to figure out why there should/can be the "s" variable which is the lower bound of the integration in the RHS of the following inequality: ## \left \|\int_{-s}^{0} A(t+r)Z(t+r) dr \right \|^{2} \leq s\int_{-s}^{0}\left \| A(t+r)Z(t+r) \right \|^{2} dr...
40. Natural SUSY-MSSM and NMSSM gluino mass bounds @LHC

Gordon Kane states that string theory predicts 1.5 TEV Gluinos. Tommaso Dorigo No deviation is seen in gluino searches. The limit extends to 1.7 TeV, thus ruling out the region favoured by Gordon Kane in a recent paper. What's the upper limit gluino masses a 13/14 TEV can produce, and what is...
41. Cantelli's Inequality and Chebyshev's Inequality

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)...
42. Integral with symmetric infinitesimal bounds

Homework Statement I'm reading something in my quantum physics book that says given a wavefunction ψ that is even, if we evaluate its integral from -ε to ε, the integral is 0. How can this be? I thought this is the property of odd functions. Homework Equations ψ=Aekx if x<0 and ψ=Be-kx if x>0...
43. Bounds of a Fourier Transform

If I have a wave function given to me in momentum space, bounded by constants, and I have to find the wave function in position space, when taking the Fourier transform, what will be my bounds in position space?
44. Origin of number of bounds in ising model

what is the origin of the number of bound (N z /2 ) in the calculating of average in ensemble in Mean Field for the Ising model?
45. Bounds of Integration for Random Oriented particle

In the Stoner-Wohlfarth model, a uniaxial, non-interacting particle is cooled to very low temperature with no exposure to an external field. Therefore, the orientation of each particle is random, if you have a group of particles. In their paper, they integrate such that: \langle \cos (\Theta...
46. Spherical Coordinates - Help me find my bounds

Homework Statement A vase is filled to the top with water of uniform density f = 1. The side profile of the barrel is given by the surface of revolution obtained by revolving the graph of g(z) = 2 + cos(z) over the z-axis, and bounded by 0 ≤ z ≤ π. Find the mass of the vase. Homework...
47. Integral Bounds: Explaining Inequalities & f(u) to f(x)

Homework Statement This is the problem with the solution: Can someone please explain how the new bounds were computed, I don't quite understand what's going on with the inequalities? Also, in the final two steps, how can the f(u) change to f(x)?
48. Help with convolution bounds

Homework Statement Mainly concerned with part (a). Here's the answer: I understand where the answers inside the bracket came from, but I don't understand how they got their bounds (-infinity to 3, 3 to 5, and 5 to infinity) Homework Equations x is the impulse function here so y(t) =...
49. Exploring Bounds on 2HD Potential: Implications and Applications

Hi all, I found that any two Higgs doublets potential should be bounded from below - at ## V \to - \infty ##. I want to know why this bound is assumed or what does it mean ? Also are there any textbooks to learn how to make this bound on any other general potential and so to constrain the...
50. Integrals with undefined bounds

Homework Statement Find the area enclosed by the equations: y=1/x and y=1/x^2 and x=2 Homework Equations N/A The Attempt at a Solution So I solved this analytically after looking at a graph of the two functions. Using integrals I got the following: ln(2)-1/2 Which is the correct answer. I...