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Functional Analysis

Region

Sketch the region consisting of all points (x, y) such that x2 + y2. You need to include all steps in calculating the resulting region. (See attachment for full question)

Consider the shaded doman D

Problem 14 ONLY 14) Consider the shaded doman D in the attached figure bounded by the simple closed... (see attachment)

Finding Extrema: Lagrange Multipliers

Use the method of Lagrange multipliers to find the indicated extremum. Let f(x,y) = 8x^2 - 24xy + y^2. Find the maximum and minimum values of the function f(x,y) subject to the constraint 8x^2 + y^2 = 1.

Minimizing F(x)

Let Q=(0,7) and R=(10,11) be given points in the plane. We want to find the point P=(x,0) on the x-axis such that the sum of distances PQ+PR is as small as possible. To solve this problem, we need to minimize the following function of x. F(x)=?? over the closed interval [a,b] where a=?? and b=??

Min/Max problem

Find the length of the shortest line from the origin to the line y=1-6x.

Convergence Problem

Please tell me if the following (see attached) series converge. This is a problem from my text book and unfortunately there are no solutions for this problem. I need justification, not just a yes it converges or no it doesn't answer.

Help with setting up problem

In the problem we are asked to solve for x and y. I can solve for the triangles but not able to use them to find the answer. can someone guide me.

Help with setting up problem

I would like some assistance in setting up this problem to solve. In the diagram Theta is 50 degrees and x is the unknown. Thank You