Bounds Definition and 169 Threads

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!!

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...

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...

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...

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: - $M\cup N$ : - $M\times N$ : - $M\cap N$ : - $M\setminus N$ : - $M\Join N$ : -...

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|...

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...

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...

Consider an example polynomial: $$ \begin{align*} P_{16}(z)&=0.0687195 z^{16}+0.787411 z^{15}+4.58749 z^{14}+17.7271 z^{13}+50.5007 z^{12}\\ &+111.995 z^{11}+199.566 z^{10}+291.128 z^9+351.292 z^8+351.927 z^7+292.066 z^6\\ &+199.046 z^5+109.514 z^4+47.2156 z^3+15.1401 z^2+3.25759 z+0.362677...

Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...

It looks as if ultra-light and super-heavy have become less likely. https://www.sciencedirect.com/science/article/pii/S0370269321000083

Hi, Planck's equation is written as E=hν where "E" is energy of a photon, "h" is Planck's constant having value 6.626 070 15 x 10-34 Js, and "ν", Greek letter nu, is frequency. Violet color has frequency range between 790–666 THz (Tera =10^12). If a violet photon of frequency 7.5 x 10^14 Hz...

I'm trying to evaluate the following integral in cylindrical coordinates. $$\int_0^6 \int_0^{\frac{\sqrt{2}}{2}}\int_x^{\sqrt{1-x^2}}e^{-x^2-y^2} \, dy \, dx \, dz$$ After attempting to set the bounds in cylindrical coordinates, I got $$\int_0^6 \int_0^{\frac{\sqrt{2}}{2}}\int_{\rho \cos\varphi...

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...

Cant get my head around the order of the upper and lower bounds for this, Is it always the higher take away the lower?

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...

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...

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...

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...

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...

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...

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...

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?

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...

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...

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...

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...

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...

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...

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...

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!

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? ##( \...

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...

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...

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 =...

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...

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...

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 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...

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?

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?

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...

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...

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)?

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) =...

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...

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...

Homework Statement I am having trouble setting up the bounds on the following two integrals: (a) The region E bounded by the paraboloid y=x2+z2 and the plane y=4. (b) The region bounded by the cylinder x2+y2=1, z=4, and the paraboloid z=1-x2-y2. Homework EquationsThe Attempt at a Solution I...

Hi, I'm interested in learning about what would be the compliment to the Variational method. I'm aware that the Variational method allows one to calculate upper bounds, but I'm wondering about methods to calculate lower bounds on energy eigenvalues. And for energies besides the ground state if...

Homework Statement Suppose that R is a partial order on A, B1 ⊆ A, B2 ⊆ A, x1 is the least upper bound of B1, and x2 is the least upper bound of B2. Prove that if B1 ⊆ B2 then x1Rx2. Homework EquationsThe Attempt at a Solution I split the proof into two different cases: case 1: x_1 is an...