Bounded Definition and 537 Threads

Homework Statement Let f_n:[a,b] -> R be a pointwise bounded, continuous family. Prove there exists an interval (c,d) < [a,b] on which f_n is uniformly bounded. Homework Equations no equations The Attempt at a Solution I'm stuck. If we have equicontinuity, then this is easy, so I'm...

So I asked my professor this question the other day, but I didn't get a clear answer. He said something about the fields being relative to each other, and so they didn't interact. Anyways, here is the setup: Suppose we have a circular conducting plate of some radius, and on this plate there...

Homework Statement Hi. I'm asked to find the volume of the solid bounded by the paraboloid 4z=x^2 + y^2 and the plane z=4 I have drawn the graph in 3D but I'm unsure of how to set up the integral. Also, how does one decide to use double integrals/triple integrals when finding volume?

Could anyone point me towards, articles, or any other reading material regarding ergodic theorem for Bounded Random Walks. 1) Consider an simple bounded (x,y) plane on which several 2-dimensional random walker are randomly assigned an (x,y) coordinate. 2) Furthermore, if 2 random walkers...

Homework Statement The question states: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. The lines are, y=lnX, y = 1, y = 2, and x = 0, rotated about the y-axis. I know how to integrate it, I just don't exactly know which...

Is the derivative operator d/dx bounded with respect to the norm <f,g> defined by integral from 0 to 1 of f g* +f'g*' where * denotes conjugation. Thank you. (Not homework)

Homework Statement Find the abs min/max values of the function f(x,y) = e1-2x2-y2 on the closed and bounded region x2 + y2 <= 1 The Attempt at a Solution First I have to find the critical points Dfx = (-4x)e1-2x2-y2 Dfy = (-2y)e1-2x2-y2 Clearly e1-2x2-y2 cannot equal 0...

Consider the region R bounded by y=9-x^2, y=0, x=0. rotate the line y=-1 I am not sure about the bounds. The outer radius is -1 , and the inner radius is -10+x^2 right? but after i do the calculation i got a negative value. does that mean i got the radius wrong?

smooth and L^2 on R^n. Will it be bounded?? Hello, If a function, say u, is smooth and L^2 on R^n. Will it be bounded?? In the case of n=1 I would say that it obviously is so. Because if it were unbounded then it wouldn't be L^2. But in the case of n=2 (or higher). I can imagine a...

what does it mean for a set to be bounded?? in the context of the hein-borel theorem i mean the mathematically rigorous definition

Homework Statement The function exp[ (x2 + y2 - xy)/(x2 + y2) ] = f(x,y) is continuous on the open first quadrant. Prove it is bounded there. Prove f cannot be extended continuously to the closed first quadrant. The Attempt at a Solution Since f is a real-valued function...

Homework Statement Theorem: If S is any bounded set in n space, and d>0 is given, then it is possible to choose a finite set of points pi in S such that every point p existing in S is within a distance d of at least one of the points p1, p2, ..., pm. Prove this theorem assuming that the...

Homework Statement If {s_n} is nondecreasing and bounded above, and L = lim s_n, prove that s_n <= L. Homework Equations The Attempt at a Solution This is one of those proofs that seems, to me, to be obvious from the proven theorem that states that the limit of a sequence is equal...

Homework Statement i) Construct a bounded closed subset of R (reals) with exactly three limit points ii) Construct a bounded closed set E contained in R for which E' (set of limit points of E) is a countable set. Homework Equations Definition of limit point used: Let A be a subset of...

Homework Statement For the following auto. first order ode: x' = x^2 - y -1 , y' = x + x*y, show that each integral curve begins inside the unit circle remains there for all future time. Homework Equations Okay, i think what needs to be shown... define a new equation r^2 = x^2 + y^2...

Homework Statement I need to find the volume of the body bounded by the following surfaces: z = x2 + y2 z = 1 - x2 - y2 Homework Equations Volume of a body between z=o and the upper surface: \iint_{D} z(x,y) dA The Attempt at a Solution Ok, this is something I need to do with...

Homework Statement Show that any non-increasing bounded from below sequence is convergent to its infimum. Homework Equations Not quite sure... is this a monotonic sequence? The Attempt at a Solution At this point I'm not even sure about which route to go. I am in need of...

Homework Statement Is the derivative operator D:L^2(0,1)\to L^2(0,1) bounded? In other words, is there a c>0 such that for all f\in L^2(0,1), \|Df\|\leq c\|f\|?Homework Equations For all f\in L^2(0,1), \|f\| = \int_0^1 |f|^2\,dx.The Attempt at a Solution I'm pretty sure the answer is no. Here's...

Homework Statement Show that the range \mathcal{R}(T) of a bounded linear operator T: X \rightarrow Y is not necessarily closed. Hint: Use the linear bounded operator T: l^{\infty} \rightarrow l^{\infty} defined by (\eta_{j}) = T x, \eta_{j} = \xi_{j}/j, x = (\xi_{j}). Homework Equations...

question: how do i find the area under f[x,y] bounded by a closed parametric curve x[t],y[t]? it doesn't look like i can use a change of variables. it seems as though double integrals only with functions where the curve is given explicitly such as y[x] or x[y].

Homework Statement A sequence b_n is said to be of bounded variation if the series \sum_{n=1}^{\infty} |b_{n+1} - b_n| converges. Prove that if b_n is of bounded variation, then the sequence b_n converges. Homework Equations The Attempt at a Solution If b_n is of bounded...

Homework Statement Determine the expression for the area bounded by a polar curve and the criterion for integrability using both Darboux and Riemann sums. Homework Equations N/A The Attempt at a Solution Any suggestions on how to correct any errors in the following proof...

Homework Statement Find the centroid of the solid bounded below by the cone z = \sqrt{3(x^2+y^2)} and bounded above the sphere x^2+y^2+z^2=36. Homework Equations Let G be the given solid and denote its volume by V_{G}=\int \int \int_{G} 1 dV. \frac{\bar{x}= \int \int \int_{G} x...

Homework Statement given a set A(subset of R(reals)) is bounded.and for all x belongs to R there exists epsilon(eps) such that {(x-eps,x+eps) intersection A} is countable..to prove A is countable Homework Equations The Attempt at a Solution...bdd set in R is totally bounded...but...

Homework Statement Find the volume of the solid T enclosed above by the sphere x^2+ y^2 + z^2 = 2 and below by the parabloid x^2 + y^2 = z Homework Equations The double integral. Possiblly polar coordinates (x = r*cos(theta) y = r*sin(theta)). z = f(x,y) The Attempt at a Solution...

Hi all, my first post so go easy on me! Doing some revision and have been tripped up on a really simple question! Where f(x) = xCos(x) Show the bound f '(x)<=6 is valid for 0<= x<=5 I suspect this is an easy solution using the intermediate value theorem! Thanks in advance, slippers

Greetings! I have a question which I hope you would like to answer. I am on my last year of high school so please bear with me. I am planning to read Griffiths' book on electrodynamics, though, so that I can fully grasp my problem. This problem is not a homework question. Let there be a...

Homework Statement A sequence (an: n \in N) is defined by an= (2n+3)/(3n+6) for all n \in N. (a) Prove that this sequence is bounded above by 2/3; (b) Prove that the sequence (an: n \in N) is monotonely increasing by showing that 0<an+1-an for all n \in N. The Attempt at a Solution...

Homework Statement Let f:C->C be an entire function such that Imf(z) <= 0 for all z in C. Prove that f is constant. Homework Equations Cauchy-Riemann equations?? The Attempt at a Solution I don't know why I haven't been able to get anywhere with this problem. I feel like I have to...

Homework Statement Find the general solution of: y''+(1/x)y'=0 and show that only constant solutions are bounded. Homework Equations The Attempt at a Solution integrating factor say a=e^(int(1/x)dr)=x so xy''+y'=0. so (xy')'=0 integrate both sides: xy'=c (c is a constant)...

centroid of the region bounded by the curve...need help! Find the centroid of the region bounded by the curve x=2-y^2 and the y-axis: my work shown: therefore if A= 2 times the integral of sqrt(2-x) dx is the M_x equal to the integral of (2-x) dx from 0 to 2? and the M_y equal to...

the question: f(x) continues on (-\infty,a] and suppose that the border \lim_{x->-\infty}f(x) exists and finite. prove that f(x) is bounded on (-\infty,a] and/or that exists x_0\epsilon(-\infty,a]=\lim _{x->-\infty }f(x) so \sup_{x\epsilon(-\infty,a]} f(x) in other words prove that f(x)...

Homework Statement Suppose that f: R -> R is continuous on R and that lim (x -> \infty+)(f(x) = 0) and lim (x -> \infty-)(f(x)=0). Prove that f is bounded on R Homework Equations I have got the proof of when f is continuous on [a,b] then f is bounded on[a,b] but I'm unsure as to whether...

A grid of 4x4 is given .__.__.__.__. | | | | | .__.__.__.__. | | | | | .__.__o__.__. | | | | | .__.__.__.__. | | | | | .__.__.__.__. A ball is located at the center of the grid which is to perform a 5 step random walk with equal probability in any...

Homework Statement I have to take an integral of x^3/(1+x^2) from zero to 1.48766439...(I have the number). Homework Equations None really. The Attempt at a Solution Well, I tried and tried, and I could not find a single way to separate the top from the bottom. Also, I tried u...

Homework Statement If f:[a,b] \rightarrow \Re is bounded then so is |f|, where |f|(x) = |f(x)|. Call f absolutely integrable if |f| is integrable on [a,b]. Give an example of a bounded function which is absolutely integrable but not integrable. Homework Equations None The Attempt at...

I cannot remember if infinity is an upper bound for a subset of R? I think so, but I want to be sure before I use it in a proof.

Homework Statement What's the derivative of the following two: \int_{a}^{h(x)}f(t)\,\mathrm{d}t \int_{u(x)}^{v(x)}f(t)\,\mathrm{d}t Homework Equations The Attempt at a Solution I thought of doing the following: \int_{h(a)}^{h(x)}f(t)\,\mathrm{d}t = \int_{a}^{x}f\circ h(u)\cdot...

need to prove that f(x) bounded if f(x) continuous in [a,+infinite] and if there's a limit while x goes to +infinite. I would really appreciate any kind of help !

Xn=(1-1/2)(1-1/4)..(1-(1/(2^n)) i tried to prove that its monotonic by : 1-1/(2^n) = (2^n-1)/2^n 2^n -1 <2^n obviously its correct the numerator of each object is smaller then the denominator. what now?? and how to prove that its bounded?

We need to find the volume of the solid bounded by the cylinder with the equation z^2 + y^2 = 4 and the plane x + y = 2, in the first octant (x,y,z all positive). Firstly, I am trying to visualize the graphs. From what I can tell, the cylinder is centered around the x-axis and has a radius...

Homework Statement http://img252.imageshack.us/img252/4844/56494936eo0.png 2. relevant equations BL = bounded linear space (or all operators which are bounded). The Attempt at a Solution I got for the first part: ||A||_{BL} =||tf(t)||_{\infty} \leq ||f||_{\infty} so ||A||_{BL} \leq 1...

in this link i written the question and how i tried to solve them http://img504.imageshack.us/img504/7371/95405842kw4.gif how to finish it??

How to show that if f is an entire function,such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i) for all z belong to C. π is pi.

Homework Statement Let X be a non-empty set and let C be the set of all bounded real functions defined on X, with the metric induced by the supremum norm: d(f,g) = ||f - g|| = sup |f(x)-g(x)| , x in X. Show that the metric space (C,d) is complete. Hint: if \{f_{n}\} is a cauchy sequence...

Homework Statement Assume \sum_{1}^{\infty} a_n is absolutely convergent and {bn} is bounded. Prove \sum_{1}^{\infty} a_n * b_n is absolutely convergent Homework Equations A series is absolutely convergent iff the sum of | an | is convergent A series is convergent if for every e...

Homework Statement Let I=[a,b] and let f:I->R be a function (not necessarily continuous) with the property that for every x in I, f is bounded in a neighborhood of x. Prove that f is bounded on IThe Attempt at a Solution I have no idea

Homework Statement http://img389.imageshack.us/img389/9272/33055553mf5.png The Attempt at a Solution Via induction: for n=1 equality holds now assume that Vn=Jn. I introduce a dummy variable b and the fundamental theorem of calculus and change order of integration: V_{n+1}f(t)...

Homework Statement Prove the any bounded open subset of R is the union of disjoint open intervals. The attempt at a solution I've seen a proof of this using equivalence classes, which is fine, but I want an unsophisticated solution, e.g. one relying on just the definitions of "bounded"...

Homework Statement Find the area of the curve 2/sqrt(x) bounded by x = 0, y = 3, y = 1 Homework Equations The textbook claims the answer is 3. The Attempt at a Solution I tried both vertical and horizontal elements, but got different answers than 3. Here's my attempt at...