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Normed Space, Compactness and Transformation

Let X be a normed space, I closed interval ( or half-open on the right) and a = inf I, b = sup I. Let h : I -> [0,infinity) be a continuous function such that integral ( from a to b ) h(t)dt < positive infinity where integral from a to b represents the improper integral when I is not closed. Let epsilon > 0 and

Volumes of Solids : Washers and Disks

Find the volume of the solid formed when the region described is revolved about the x axis using washers and disks. 14) the region under the curve y= cubed root of x on the interval 0&#8804;x&#8804;8. 16) the region bounded by the lines x=0, x=1, y=x+1, and y=x+2. 20) the region bounded by the curves y=e^x and y=e^-x on


1. Use integration to find a general solution of the differential equation. dy / dx = (x-2)/ x = 1 - 2/x 2.Solve the differential equation. dy / dx = x + 2

Hilbert Space : Absolute Continuity

Let H be the collection of all absolutely continuous functions f [0,1] -> F, where F denotes either real or complex field ) such that f (0) = 0 and . If for f andg in H, then H is a Hilbert space. Please see the attached file for the fully formatted problem.

Solving a Pfaffian equation for a complete integral

Hello. Thank you for taking the time to help me. I cannot use mathematical symbols, thus, * will denote a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. To simplify things, I will let p=u*x and q=u*y. Furthermore, I will use ^ to denote a power. For example, x^2 means x squared. Also,

Green's function

Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts): I need to construct Green's function for the Dirichlet problem (Laplace's equation) in the upper half plane R={(x,y) : y>0} and I must derive Poisson's integral formula for the half plane.

Integration (10 Problems)

A) (e^x/((e^x+2)^(1/2))dx between 0.5,0 b) (x^2/((1-2x^3)^(1/2))dx c) (sin^5(x))dx between ((3.14/2),0) d) (x^2 cos(x))dx e) (1/((2x+5)(1-3x)))dx f) (3x-4/((x-2)(x+1))) dx between the limits 5,4 g) (4x.e^(-4x))dx between the limits 1,0 h) (3x.sin(3x))dx i) (sin(4x) - 4cos(3x)

Business Statistics

Please see attached. Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much. I would like for you to show me all of your work/calculations and the correct answer to each problem. For Exercise 2, find the mode of the probabili

Laplace transformations

I am looking for the solution of this transformation I need a detailed solution. Also I would like to see the original formula for the Laplace transformations needed. If f(t) is a periodic, continuous function with period T>0, show that its Laplace transform is... Please see attached.

Computing areas and volumes using multiple integrals.

(1) Find the volume of the solid bounded by the paraboloid x2 + y2 = 2z, the plane z = 0 and the cylinder x2 + y2 = 9. (2) Find the volume of the region in the first octant bounded by x + 2y + 3z = 6. (3) Find the area of the solid that is bounded by the cylinders x2+z2 = r2 and y2+z2 = r2. (4) Find the volume enclosed by t