Bounded Definition and 514 Threads

Its a question that I had from a friend in the past. I had tried solving it but to no avail. Have tried integration and stuff like that, but I think there is an easier way to solve this question. Question -> Square of 7cm, find the shaded area...

Hello all, I am a bit confused by the concept of "bounded almost surely". If a random variable X(\omega) is bounded a.s., so this means (i) X \leq K for some constant K ? or some K(\omega) ? Also, if it is bounded almost surely, does that mean it is also bounded in L^{p} ? Apparently if...

I have a sequence where s_1 can take any value and then s_{n+1}=\frac{s_n+10}{s_n+1} How do I show a sequence like this is bounded?

Having a hard time understanding this example from a book: The function f(x) = 1/x is locally bounded at each point x in the set E = (0,1). Let x \in (0,1). Take \delta_x = x/2, M_x = 2/x. Then f(t) = 1/t <= 2/x = M_x if x/2 = x-\delta_x < t < x + \delta_x This argument is false since...

Homework Statement Find the average value of z for a the spherical surface of radius R that resides above the x-y plane. Homework Equations Equation of a sphere x^2+y^2+z^2 = R^2 The Attempt at a Solution I rearrange the equation above and do a double integral z_{total} = \int...

Homework Statement 1. f(z) is a function that is analytic on all of the complex plane, and mod(f)<=mod(z). Prove that f=cz. 2. f(z) is analytic on all of the complex plane, and mod(f)<= sqrt(mod(z)). Prove that f is constant Homework Equations Liouvilles thm: the only bounded entire...

Homework Statement A = \left\{(x,y): 0\leq xy \leq 1\right\}, A \in R^{2} I'm trying to determine if this set is bounded and/or closed. Homework Equations if X = (x,y) euclidean metric: ||X|| = \sqrt{x^{2}+y^{2}} The Attempt at a Solution I know a bounded set =>...

Let f is monotone increasing, bounded, and differentiable on (a,inf) Then does it necessarily follow that lim(f'(x),x,inf)=0 ? It is hard to guess intuitively or imagine a counterexample...

Homework Statement find the Area Bounded by the two curves, y=|x+1|, y= - ( x+1)2 + 6 Homework Equations y=|x+1|, y= - ( x+1)2 + 6 The Attempt at a SolutionA= Integration of | f (x) - g(x) | x+1= f(x) -(x+1)2 + 6= g(x) getting the limit of integration: x+1= - (x+1)2 + 6 x2 + 3x - 4=0...

Homework Statement Let f ba analytic function on 0< |z| < 1 and suppose |f(z)| <= 4|z|^1.1 for all 0<|z|<1. Prove that |f(1/2)| <= 1 Homework Equations The Attempt at a Solution I tried to prove it be cauchy integral formula but I got |f(1/2)|< 8 r ^1.1 r<1

Homework Statement I have a problem where the graph of the equation is below the x-axis at x=0, crosses the x-axis at x=2, and is above at x=5. To find the area of this would I just split the interval into two parts, find both areas, and then add them? Or would I simply ignore the part of the...

Homework Statement Use the left endpoint graph with the given number of rectangles to approximate the area bounded by the curve f (x), the x-axis, and the line x = 4. f(x)=x2+x Homework Equations No idea. The Attempt at a Solution Once again, not a clue how to start this.

Homework Statement Attached question Homework Equations The Attempt at a Solution I tried rearranging S1 for Z then using Maple to plot it, which gave me a cone extending from the point z=1. For S2, would I have to plot it twice? once for <1 and once for =1? I have no...

Not really homework, but a textbook-style question... Homework Statement Is every subset of a totally bounded set (of a metric space) totally bounded? Homework Equations F is said to be totally bounded if, for every \epsilon>0, there's a finite subset F_0\subset F such that...

Hello--- I've been working on a problem which requires the numerical evaluation of an improper integral. I would like to transform the limits of integration on [0,\infty) to the bounded region [a,b] by replacing the variable \omega with another variable. Here is the integral...

Using polar coordinates to find the volume of a bounded solid[Solved] I found the equation of the boundary circle by setting z to 4 in the paraboloid. Then I did some work to get polar coords: x^2+y^2 = 1 x^2+y^2 = r^2 1-x^2-y^2 = 1-r^2 Then I set up my integral as such...

I asked by someone. But I can't answer to it. \sum^{\infty}_{1}(-1)^n*(1+\frac{1}{n})^n Is this series bounded? I can't do anything about that.

Homework Statement Part A) Establish which of the following combinations of particles can exist in a state of I=1 : a) \pi^0\pi^0 b) \pi^+\pi^- c) \pi^+\pi^+ d) \Sigma^0\pi^0 e) \Lambda^0\pi^0 Part B) of the problem is: In what states of isospin may exist the following systems? f)...

Homework Statement Bounded by the cylinders x2 + y2 = r2 and y2 + z2 = r2 We're supposed to stick to double integrals as triple integrals are taught in a later section. The Attempt at a Solution Edit: Alright, I think I go to the right answer. x = sqrt(r2 - y2) z = sqrt(r[SUP2[/SUP] - y2)...

Is a bounded set synonymous to a set that goes to infinity? I feel like unless a set is (-infinity, n) or [n, infinity) it is not going to be unbounded. The other thing that I was wondering is can a set be neither open nor closed AND unbounded? Doesn't the definition of open/closed imply...

Homework Statement Hey, the original question is not in english, so I am translating. So just to make sure I'm understood, i take convex to mean that the graph of the function is below the tangent. The question: Let F be a convex function and F is bounded from above by some number C, prove...

Homework Statement Let x_m = 1 + \frac{1}{2} + \frac{1}{3} + ... \frac{1}{m}, m \in N. Prove x_m is not bounded above and therefore x_m does not converge.Homework Equations We know from our class an important theorem stating that: If sequence converges then the sequence is bounded. Thus we...

hi. i'm reading "quantum mechanics in hilbert space" and a don't get a basic point for bounded operators. def. 1 a set S in a normed space N is bounded if there is a constant C such that \left\| f \right\| \leq C ~~~~~ \forall f \in S def. 2 a transformation is called bounded if it maps...

Homework Statement If f(t) transforms into F(s), so that \[ F(s) = \frac{{s + 1}}{{s^2 + as + 1}},a \in \] , prove that if a < 0, the function f(t) isn't bounded, and if a >= 0, it is bounded. Prove that if -2 < a < 2, f(t) oscilates. The Attempt at a Solution I honestly have...

Homework Statement Assume the theorem that a continuous bounded function on a closed interval is bounded and attains its bounds. Prove that if f: R -> R is continuous and tends to +\infty as x tends to +/- \infty then there exists an x0 in R such that f(x) \geq f(x0) for all x in R...

Homework Statement E1 = {pn(t) = nt(1-t)n:n in N}; E2 = {pn(t) = t + (1/2)t2 +...+(1/n)tn: n in N}; where N is set of natural numbers is the polynomial bounded w.r.t the supremum norm on P[0,1]? Homework Equations supremum norm = ||*|| = sup{|pn(t)|: t in [0,1]} The Attempt...

Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...

Homework Statement f is of bounded variation on [a;b] if there exist a number K such that \sum^{n}_{k=1}|f(ak)-f(ak-1)| \leqK a=a_0<a_1<...<a_n=b; the smallest K is the total variation of f I need to prove that 2) if f is of bounded variation on [a;b], then it is integrable on [a;b] 2...

hi, i have a hard problem, i guess so, i am looking for any help g(x) is a bounded Lebesgue measurable function that is periodic i.e. g(x)=g(x+p). Then for every f \in L^1(\Re) lim_{n\rightarrow \infty}\int_{\Re}f(x)g(nx) dx=(\int_{\Re}f(x)dx)((1/p){\int_{0}^{p}g(x) dx) thanks for...

In many statements in probability, there is an assumption like bounded fourth moment, so is there any random variable which has unbounded fourth moment?

Homework Statement Given this ode system: x' = 2x+y-7e^(-t) -3 y'= -x+2y-1 Find all the bounded soloution in [a,infinity) when a is a real number... I'm not really sure what is a sufficient condition for bounded soloution in this question...Maybe there's something we can do and then we...

Hello, Just reading an essay about spherical harmonics and it says that spherical harmonic form a complete orthonormal basis set of functions over the sphere and can be used to represent any bounded single-valued function over a sphere. I am not sure I understand why we can only represent...

In general, would it be true that if a set is bounded, there must also be a supremum for the set? Too obvious, perhaps?

Homework Statement Find area of region bounded by curve with equation y=e^2x , the x-axis and the lines x=-ln3 and x=-ln2. Homework Equations log. law + integration The Attempt at a Solution well here is how i started this: y=e^2x after integration (1/2e^2x)...

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?

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 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...