Bounded Definition and 514 Threads

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

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...

Homework Statement Let f:[a, b] -> R have a limit at each x in [a, b]. Prove that f is bounded. Homework Equations None The Attempt at a Solution No idea on how to start the proof. Completely lost. Thank you

Homework Statement Give an example of a function f : R -> R where f is continuous and bounded but not uniformly continuous. Homework Equations A function f : D -> R and R contains D, with Xo in D, and | X - Xo | < delta (X in D), implies | f(X) - f(Xo) | < epsilon. Then f is continuous...

question 1 : Prove that a sequence which is bounded above cannot tend to infinity What i did was state the definition ... but I'm trying to proof by contradiction. So i first suppose that a(n) tends to infinity , then a(n) > C . But since it is bounded above , C < or = to U , where U is the...

Homework Statement x is an upper bound for the set Y. Prove that x = sup(Y) (least upper bound) if and only if for every e > 0, there is some y in Y (depending on e) such that x < y + e (e in this case is every positive real number) The Attempt at a Solution since for every y in...

Is the set S = {(x,y): |x| + |y| <= 2} bounded? If so how do i prove it? looking at the graph i believe that S is bounded by 2 and -2, but I'm not sure if I'm correct and i don't know how to prove it. thanks!

Homework Statement find the area bounded by the parabolas y=2x^2-x-15 and y=x^2-4x-5 Homework Equations The Attempt at a Solution x^2+3x-10=0 I got x = 2 and x = -5; is that right? If so, why do I keep getting an area of 76.17 when I integrate from -5 to 2? I end up with...

Homework Statement Suppose that the sequence {an}converges. Show that the sequence {an} is bounded. The Attempt at a Solution Since the sequence converges, for every delta>0, there must exist a number N such that for every n>=N, |an - x|< delta. Therefore, for n>=N, -delta+x < an < delta...

Suppose I have a 2nd order differential equation a_1y''(x)+a_2y'(x)+a_3y(x)+a_4=0 and two conditions y(0), y'(0). Then is there any theorem which gives us the condition under which the solution y(x) will be bounded? Note that x-range is entire real line. This is a general version of the...

If I were to travel from point a to point b at the speed of light, given that a and b are real, I would travel a constant distance through space, and because space is bonded with time, traveling from point a to point b at the speed of light would result in a constant distance in time. It may...

Homework Statement A cruve has the equation y = x{3} - 8x^{2} + 20x . The curve has stationary points A and B. There is a line through B parallel to y-axis and meets the x-axis at the point N. The region R is bounded by the curve , the x-axis and the line from A to N. Find the exact area under...

I just encountered a claim, that for any given metric space (X,d), there exists another topologically equivalent metric d' so that (X,d') is bounded. Anyone knowing anything about the proof for this?

Homework Statement Let f be a continuous mapping from metric spaces X to Y. K \subset Yis compact. Is f^{-1}(K) bounded? Homework Equations Theorem 4.8 Corollary (Rudin) A mapping f of a metric space X into Y is continuous iff f^{-1}(C) is closed in X for every closed set C in Y...

Let the random variable X have the probability density function f(x). Suppose f(x) is continuous over its domain and Var[X] is bounded away from zero: 0 < c < Var[X]. Claim: f(x) is bounded over its domain. Is this claim true? I don't think a counterexample like X ~ ChiSq_1 applies...

If the universe is bounded then there will be an absolute frame of reference. This could be found by summing all the frames of reference up to the unltimate one ie your in a car traveling on road that's on the earh which is spinning on it axis and simutaneously moving about the sun . The sun...

1. Find the area of the region bounded by x^2 - xy + y^2 = 2: a)let x = au + bv, y= au - bv therefore, 3b^2v^2 + a^2u^2 = 2 b) Choose a and b such that u^2 + v^2 = 1, therefore, a = sqrt 2 & b = (sqrt 6)/3 c) Applying these results and changing variables into u and v, evaluate the...

Homework Statement Prove that every compact set is bounded. Homework Equations The usual compactness stuff - a compact set in a metric space X is one that, for every open cover, there is a finite subcover. The Attempt at a Solution I'm really hesitant about this question because my...

Homework Statement If A and B are bounded sets, then A U B is a bounded set. (Prove this statement) Homework Equations Definition of Union is a given. A set A is bounded iff there exists some real value m such that lxl < m for all element x found in A. The Attempt at a...

Hello, I am interested in the average behaviour of the log of a function. I know the average of the function over the range of interest: F = \frac{1}{(b-a)} \int_a^b f(x) dx. I also know that f(x) is convex and bounded from below by 1. I want to know the average \frac{1}{(b-a)}...

Let H be a Hilbert space and A: H-> H be a Linear Bounded Operator. Show that A can be written as A=B+C where B and C are Linear Bounded Operators and B is self-adjoint and C is skew. This is suppose to be an easy question but I'm not sure where to start. I know that self-adjoint is (B*=B)...

Dear friends, I just joined the forums, and I'm looking forward to being a part of this online community. This semester, I signed up for Analysis II. I'm a math major, so I should be able to understand pretty much everything you say (hopefully). However, I'd really appreciate it if you try...