Bounds Definition and 182 Threads

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...

Convergence of Divergent Series Whose Sequence Has a Limit Homework Statement Suppose ∑a_{n} is a series with lim a_{n} = L ≠ 0. Obviously this diverges since L ≠ 0. Suppose we make the new series, ∑(a_{n} - L). My question is this: is there some sufficient condition we could put solely...

Hi all I have another upper/low bound question, i have attached the question to this thread. The bit i am having trouble with is part (II) i.e. calculate the upper bound of H. I attempted this and got: - (24.45^2)/(2*9.85) = 30.34530457 H = 30.3 (3 sig fig) The problem is that...

Hi all I am studying for a maths test regarding upper and lower bounds, i have found a list of questions which i have attempted, i wa hoping someone could confirm if my answers are correct. 1. The weight of a bag of potatoes is 25 kg, correct to the nearest kg. (a) Write down the smallest...

So, I have a bunch of errors which need resolving here but majority are based on the "out of bounds" error and hence the topic title :). Would be great if you are able to help me resolve the errors. Quite a newbie with fortran. So please bear with any silly questions that I may throw at you...

Hello, I'm studying for the exam and in the previous one there's a question like: Homework Statement Find the value of 1/(2*i*pi) ∫ exp(s*u)/s² ds for s from 1-i∞ to 1+i∞ What is the way to solve integrals with complex bounds ? Is it to make a variable change to get real bounds, like...

Hi everyone, :) What is a Tight Upper Bound? Is it the least upper bound? But then tight upper bound will be equivalent to the supremum. :confused:

Homework Statement Let E be a non-empty subset of the real numbers R. Define carefully each of the terms (i) 'y is an upper bound for E' and (ii) 'y is the least upper bound for E' Homework Equations The Attempt at a Solution I've just started doing analysis and I'm unsure how...

In a semiconductor, is the chemical potential of electrons limited to take values only between the valence band maximum and conduction band minimum? Are there circumstances where it can cross these bounds?

So here I am trying to solve Rayleigh's differential equation using Rungen-Kutta 4th order analytic method. This is what the exercise gives me: X(0 to 40), Y1(0)=0.1, Y2(0)=0, H=0.1, μ=0.5 This is what I ve written and gives me this error: IMPLICIT REAL*8(A-K,O-Z) DIMENSION...

Homework Statement Given the tridiagonal matrix T_{n} 2+x 1 0 0 1 2+x 1 0 0 1 2+x 1 etc. Derive an upper bound on the infinity norm ||T_{n}^{-1}|| and also derive an upper bound on the condition number of the matrix The Attempt at a Solution This is not...

Hi to all. I am programing a new code for some calculation and i have detected a strange issue. I have my all arrays strictly defined for example real, dimension(-2:2,-3:2) A, B complex, dimension(-2:2,1:2) C In my time dependend calculations i expect the matrix element C(-2,1) to...

Hey, I was reading about this is in "Additive Combinatorics" (Additive Combinatorics (Cambridge Studies in Advanced Mathematics): Terence Tao, Van H. Vu: 9780521136563: Amazon.com: Books) on pg. 4 when I went to the references and found this paper (http://renyi.mta.hu/~p_erdos/1965-02.pdf) which...

Hello, I'm struggling to figure out the syntax/method (on a TI-89) for finding the area of a curve bounded by the x and y-axis (and the curve) in a particular quadrant. Respectfully submitted, McFail

Homework Statement Given a set A that contains all numbers of the form, n/(n+1), where n is a positive integer, a.explain why the number 1.1 is not the lub of A. b.explain why the number 0.95 is no the lub of A. Homework Equations The Attempt at a Solution a. Suppose 1.1 is...

Homework Statement Define a1=1, and for every n>1, an+1 = an + \frac{1}{an}. Prove that 20 < a200 < 24The Attempt at a Solution I tried a few things to no avail. First, I showed that this is an increasing function by showing an+1 > an. I tried finding a limit, by saying if...

Hello! Unfortunately, I have not spent as much time as I should have on limits, or sequences, or their properties. In trying to work on a number theory math proof I have come across the following: I have an infinite sequence of numbers, all between 0 and 1 inclusive. I know that the limit of...

I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are I_3 \pm dI_3 The problem is that i'd lke...

Homework Statement Assume happiness can be measured on a scale from -10 (very unhappy) to 10 (extremely happy). Let D denote the set of possible ways to live one day. For each way of living a dayd∈D define a function h_d:[0,24]⟶[−10,10] to be equal to the value of happiness at each point...

When taking a definite integral that is bound by two points a and x where a is a constant and x is a variable, which quantity do I consider the upper limit of the integral and which quantity is the lower limit? \int^a_x x this integral is written as -\int^x_a x in my book. When I use...

Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves y= e-2x^2, y=0, x=0, x=1. Should the bounds for the problem be taken from the y-axis or the x-axis? I think that the integral for this problem would be: ∏∫(e-2x^2)dx , is this correct

∞ ∫ x^3 dx =∫ x^3 dx+∫x^3dx -∞ I split up integral and got (x^4)/4 and infinity when evaluating using limits. does the integral converge to zero or diverge to infinity minus infinity? would really appreciate help answering this question. Thanks

Homework Statement Find the potential difference between V(P) - V(R) and V(c) - V(a) Homework Equations Electric potential: V(a) - V(b) = \int^{b}_{a}E*dr V(b) - v(a) = -\int^{a}_{b}E*dr Fundamental Theorem of Calculus: F(b) - F(a) = \int^{b}_{a}f(x)dx The Attempt at...

hey everyone is integrating from -L<x<L the same as integrating over -L \leq x \leq L? I am looking for a rigorous response, so if you have time could you explain why, rather than simply yes or no? thanks!

Recently I am studying about theorems regarding to polynomial equations and encounter the lower and upper bounds theorem. Which states that if a<0 and P(a) not equals 0, and dividing P(x) by (x-a) leads to coefficients that alternate signs, then a is a lower bound of all the roots of P(x)=0. The...

Hi, I am running a code in MATLAB process 8 columns and over 500 rows of data but i get the above error. With 6 columns, the code works well. Your help is important.

Homework Statement For any random variable X, prove that P{X\geq0}\leqinf[ E[ phi(t) : t \geq 0] \leq 1 where phi(t) = E[exp(tX)] o<phi(t)\leq∞ Homework Equations The Attempt at a Solution I am not sure how to begin this. Any hints to get started would be greatly appreciated.

And in general, always been bad at it. If original bounds are ∫pi/3 to 0 and I am changing the bounds because I'm U-substituting. My subtitution is u=secx so is it when cos = pi/3 and 0 or am I wrong? so the new bound would be from pi/2 to pi/3..?

So we are estimated derivatives using a three point formula in class and the giving bounds for the error. I was given a table of x1=1.1, x2=1.2, x3=1.3, x4=1.4. I have to find an error bound to estimate the error for x=1.1 and 1.3 for f(x)=ex In class we did x=1.1 as follows...

If n>m>1, find upper and lower bounds for n!/m! Answer: upper bound = {[(n+1)^(n+1)]/[(m+1)^(m+1)]}*e^(-(n-m)) lower bound = [(n^n)/(m^m)]*e^(-(n-m)) This is from a chapter on finding bounds for sum of series. Can someone please explain how to arrive at the answer? Thanks!

Hi there! I always think whether I am posting this correctly, or this belongs to the homework section. If so, my apologies. I am trying to understand the solutions for a problem in Spicak Calculus, 3^{rd} edition. #8-13 The Problem: "Let A and B bt two nonempty sets of numbers...

this is a riemann sum question and i need help with part 2 let Sn denote the finite sum 1+2^ 3/2 +...+n^ 3/2 i) use suitable upper and lower riemann sums for the function f(x)=x^3/2 on the interval [0,100] to prove that S99<J<100 ummm i did this and found 40000<J<41000 II) hence, or...

Homework Statement I am making a very, very simple program that takes in the date (of type string) from the user in the form DD/MM/YYYY. It then confirms whether or not the date is legitimate or not. For example, 09/07/2012 is valid, but 09/17/2012 is not valid. My program compiles...

Homework Statement My first problem is with 2ia) and 2ib), I got the correct answer, although not happy with my understanding of it. http://img826.imageshack.us/img826/1038/443pr.jpg The Attempt at a Solution (2ia and 2ib) The region that's of concern is the upper part between y = x^2 and...

[ T'' ] = [ T ] [ T' ] [ T'' ] = [ ( γ'' ) , ( - γ'' β'' ) ] [ ( - γ'' β'' ) , ( γ'' ) ] γ'' = γ γ' ( 1 + β β' ) → no problem, proven to be b/w [ 1 , ∞ ) β'' = ( β + β' ) / ( 1 + β β' ) → can't figure out how to prove it's b/w [ 0 , 1 )

Homework Statement Find the volume of the solid that lies above the cone z = root(x2 + y2) and below the sphere x2 + y2 + x2 = z. Homework Equations x2 + y2 + x2 = ρ2 The Attempt at a Solution The main issue I have with this question is finding what the boundary of integration is for ρ. I...

Homework Statement a. Use the trapezoidal rule with n = 4 subintervals to estimate \int_0^2 x^2 dx. b. Use the error bound to find the bound for the error. c. Compute the integral exactly. d. Verify the error is no more than the error bound.Homework Equations Here, based on the problem, a...

I don't understand the bounds of the partial sum. $$ \prod_{n=0}^N(1+z^{2^n}) =\sum_{n=0}^{2^{N+1}-1}z^n = \frac{1-z^{2^{N+1}}}{1-z} $$ How does it go from N in the product to $2^{N+1}-1$ in the sum?

Homework Statement I want to estimate f(x)=\ln (\frac{1}{1+x}) on the interval (1/10,1) with the error on the approximation being no more than 0.1. Homework Equations http://en.wikipedia.org/wiki/Taylor's_theorem#Example The Attempt at a Solution Following the example from Wikipedia, I...

#Upper bounds of a given set In my analysis book it says: "If a set has a upper bound, there are infinitely many upper bounds". Why is this correct? If you have some finite set, won't there be just one?

Homework Statement Find the least upper bound and greatest lower bound (if they exist) of the following sets and state whether they belong to the set: a. {1/n:n\in"Natural Number"} b. {x\in"Rational Number":0≤x≤√5 c. {x irrational:√2≤x2} d. {(1/n)+(-1)n:n\in"Natural Number"}...

Homework Statement Hi all, just a quick question here - the setup is as follows: X is a random variable, X \sim \operatorname{Bin}(m,p) where p=2^{-\sqrt{\log n}}(\log n)^2 and m \geq 2^{\sqrt{\log n}}c for constants c, n (n "large" here). I wish to show that \mathbb{P}(X < c) \leq e^{-(\log...

Homework Statement How to determine the integral bounds of phi in spherical polar coordinates. Please see my exact question at the end of page 2 of 2 in attachments. Homework Equations Please see my attachments The Attempt at a Solution Please see my attachments.

Homework Statement I just want to show that given x<0, \frac{x-1}{x-2} <1. The Attempt at a Solution I don't know why I am having trouble with this! I feel like this is so easy! So if x<0, then we know x-1<-1, x-2<-2 . So \frac{-1}{2}<\frac{1}{x-2} and...

Homework Statement a) Derive a Taylor series with n+1 terms and the associated truncation error for the function f(x)=(log(x)-x+1)/(x-1)^2 b) Construct an expression that bounds the truncation error, assuming n > 2, for a given value of x 2. The attempt at a solution a) So I came up with the...

I've come across the bounds on zeros theorem in my algebra book, but they don't seem to try to offer proof for it. Does this proof require calculus?

Homework Statement The problem given: Homework Equations The Attempt at a Solution I need an x^2 in there to do the inner integral. I'm having a bit of trouble figuring out how the bounds are defined. X goes from 1 to y/2 and y goes from 0 to 2. So does that mean x goes from 1 to 2x?

Homework Statement Sketch the solid whose volume is given by the following integral and then evaluate this integral: ∫(0≤r≤2)∫(0≤θ≤2π)∫(0≤z≤r) (r) dzdθdrThe Attempt at a Solution So, I kind of cheated and evaluated the integral first. So I have ∫(0≤z≤r) (r) dz = rz, from z=0 to z=r, which I...