Bounds Definition and 169 Threads

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...

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...

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:

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...

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

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...

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...

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...

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

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...

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...

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...

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)<=...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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}...

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...

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...

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...

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...

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

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...

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...

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...

(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??

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...

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...

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...

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...

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...

Hi guys, Im currently revising for my exams and I encountered a problem I hope someone will be able to help me with. Homework Statement Find the volume of the region of space bounded by: The planes x=0, y=0, z=0, z=3-2x+y and the surface y=1-x^2 Homework Equations \int \int \int _R...

[SOLVED] Upper Bounds Integration Homework Statement Integrate y=4x from 2 to 5 using the limit with circumscribed rectangles. Homework Equations A=lim(n to inf.) Summation of f(xsubi) times delta (xsubi) The Attempt at a Solution A=lim(4/n)(4/n)(4)(2+3+4+...+(n+1))...

Before we start, can you just explain how to start me off? I understand the idea of all limits, just a few tricky ones that were assigned for homework. (note: ALL limits are x --> infinity) Homework Statement lim ^{}\frac{10}{x}lim \frac{x^{2}+a^{2}}{x^{3}+a^{3}}lim (1 - r^{x}) , |r| < 1...

Hey I'm typing out my math homework, and I've run into some notation that I'm kind of confused about: I need to know how to show the bounds of an integral after you've taken the antiderivative. Kind of like this: Integral (bounds: 0 to 2) of x^2 = [1/3x^3] (0 to 2). The actual...

If I have a function f(z) such that limit z --> infinity is finite what do I know about that function? Is it "bounded" or am I still confused about what "bounded" means?

1.with the function: f(x) = x^2e^-3x a)find f'(x) and f''(x) b)find the critical points of f(x) c)use the derivative to determine where f(x) is increasing and decreasing. d)use the second derivative to determine where f(x) is concave up and concave down. Identify any points of...

Homework Statement A function is decreasing if f(x_{1}) > f(x_{2}) whenever x_{1} < x_{2}, and x_{1}, x_{2} \epsilon \Re a) Show that the set {f(x) : x < a} is bounded below b) Prove that lim (as x goes to a) f(x) = glb{f(x) : x < a} (hint: show that for any \epsilon > 0, there exists...