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Functional Analysis

Weather balloon rising

A weather balloon that is rising vertically is observed from a point on the ground 300ft from the spot directly beneath the balloon. At what rate is the balloon rising when the angle between the ground and the observer's line of sight is 45 degrees and is increasing at 1 degree per second?

Mean Value Theorem

10. Does the function , , satisfy the hypotheses of the Mean Value Theorem? Find such that is the slope of the secant line passing through , and . Please see the attached file for the fully formatted problems.

Compact Subset of R^m with Convergent Sequences

Please help with the following problem. Let A be a proper subset of R^m. A is compact, x in A, (x_n) sequence in A, every convergent subsequence of (x_n) converges to x. (a) Prove the sequence (x_n) converges. Is this because all the subsequences converge to the same limit? (b) If A is not compact, show that (a

Transfer Function Analysis and Models

Please see the attached file for the fully formatted problems. Two identical stirred tanks with a recycle stream are connected as shown in the diagram below: Fr CAi,Fi CA1

Asymptotes

Find all vertical and horizontal asymptotes of f(x) = (x^2+ 4)/(x^2- 4x-12) Please show steps & graph if applicable!

Asymptotes

Explain and contrast the types of asymptotes considered for rational functions.

Vectors : Divergence, Gradients and Curls

1) V(x, y, z) = (x + y + z)2 i + (x + y)2 j + x2 k. Find div V(3, 2, 4) ≡ ∇? V (3, 2, 4) 2) F (x, y) = xe2y i + y/(x + y) j. Find ∇ ? F (4, 0) 3) F (x, y, z) = -yz i + xz j - xy k. Find curl F (1, 2, 5) = ∇×F ( 1, 2, 5)

Green's Theorem Enclosed Curves

Use Green's Thereom to find the area enclosed by the curve: {abs(x)}^(1/2) + {abs(y)}^(1/2) = 1. It is important that you solve this problem using Green's Method because that is how my professor prefers it. I know that you have to make the above statement true and switch to a different set of coordinates. Something al

Equation of ellipse and hyperbola

1 Find an equation of the ellipse with the center (0,0) , vertical major axis 14 and minor axis 10. 2 Find an equation for the hyperbola with the focus (11,12) and asymptotes 4x-3y=18 and 4x+3y=30. 3 Find the arc length of the curve given by x = sin t - cos t, y = sin t + cos t, pi/1 <= t <= 3pi/4

Polar and Rectangular Coordinates

1 Express the polar equation r^2 = 2cos2&#920; in rectangular form. 2 Find the total area enclosed by the graph of the polar equation r = 1 + cos2&#920;

Finding Area of a Region Bounded by a Line and a Curve

Sketch the region bounded by the graph of the functions and find the area of the region 1) f(x) = - x^2+ 4x + 2, g(x) = x + 2 2) f(y) = y(2 - y), g(y) = -y 3) f(x) = 3^x, g(x) = 2x + 1 keywords: integration, integrates, integrals, integrating, double, triple, multiple

Finding Absolute Minimum

Determine the absolute minimum of the function f(x) = x^3 - 3x - 1 on the interval [0, 4]. Make sure to show all work that is involved.

amplitude of resultant wave after superimposition

Two vibrations, x1 = 3 sin(10t + pi/6) and x2 = 2 cos(10t - pi/6) where t is in seconds, are superimposed. determine the time at which the amplitude of the resultant vibration, x1 + x2, first reaches a value of 2.

Functional Analysis

Attachment file. Let X be a normed space and . Show that if for every bounded linear functional f on X , then .

A Discussion On Rolle's Theorem

Please solve the following with as much explanation of each step as possible. Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0. Find an interval for the function g over which Rolle's

Weak Convergence

Please explain why the following sequence for otherwise is an example of a sequence in such that weakly, but not strongly. Please see the attached file for the fully formatted problem.

Poles & Singularities

Classify the behavior at infinity (analytic, pole, zero, or essential singularity; if a zero or pole, give its order) of the following functions: f1(z) = (z^3 + i)/z f2(z) = e^(tan(1/z))

Polar coordinates

X and y represents rectangular coordinates. What is the given equation using polar coordinates (r, theta). x^2 = 4y

Area, volume, and expantion

A.) let A be the area of a circle of radius r that is changing w/ respect to time. if dr/dt is a constant, is dA/dt a constant, explain. b.) let V be the volume of a sphere of radius r that is changing w/ respect to time. If dr/dt is constant, is dV/dt constant, explain. c.) All edges of a cube are expanding at a rate of

Single Residue : Interior to Closed Contour

5. Let the degress of the polynomials {see attachment} be such that m [less than or equal to] n+2. Use the theorem in Sec. 64 {see attachment} to show that if all of the zeros of Q(z) are interior to a simple closed contour C, then {see attachment} Please specify the terms that you use if necessary and clearly explain each

Polar coordinates

Polar coordinates o a particular point are r=4, 0=pi/3. I need to ind the rectangular coordinates of the point. (x,y)=?