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# Functional Analysis

### Find the area of the surfaces.

1.)The part of the hyperbolic paraboloid z= y^2 - x^2 that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 4 2.)The part of the sphere x^2 + y^2 + z^2 = a^2 that lies within the cylinder x^2 + y^2 = ax and above the xy-plane

### If lines are drawn on a map, a triangle can be formed by the cities of New York City, ...

If lines are drawn on a map, a triangle can be formed by the cities of New York City, Washington, D.C., and Buffalo, New York. On the map, the distance between New York City and Washington, D.C. is 2.1 cm, New York to Buffalo is 2.5 cm, and from Buffalo to Washington D.C. it is approximately 2.85 cm. If the actual straight-line

### Symmetry

See attachment How many lines of symmetry....

### 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?

### Polar Coordinates with Eule'rs Identity

Write a function to convert a rectangular form of a complete number in to it's polar form using the Euler identity.

### Types of Singularity Residues

What type of singularity does have at z=0? Find the residue of at the singularity . (see attached for equations)

### Logarithmic and Exponential Functions Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems. 1. If y = c^x express x in terms of y. (c is a positive constant) 2. a) Sketch the graph of y = 5^x for ?2 < x < 3, clearly showing the key features of this exponential function. (b) On the same graph, sketch the function y = log5 x. Explain the relationship

### Mean Value Theorem Problems

Please help with attached problem #12. Verify that the function satisfies the hypothesis of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. 12. f(x) x^3 + x -1, [0, 2]

### Contour map

F(x,y)= x+y/x-y f(x,y)= y - cos(x) Draw a contour map of each of the functions showing several level curves.

### Logarithm function - Deliverable Length: 2-4 paragraphs Details: Many different kinds of data can be modeled or measured easily using exponential and logarithmic functions. For example, consider ideal gases: Pressure versus volume give a curved plot, but a log graph of pressure versus volume provides a linear plot that is easier to interpret. Log plots are also used in the study of the rates of reactions; for many reactions, the log of remaining reactant concentration versus time is linear. For this Discussion Board, use the Library and other resources to find at least two examples of scientific data that are measured and reported using log scales. Examples can be found in such fields as chemistry, astronomy, and geology.

Deliverable Length: 2-4 paragraphs Details: Many different kinds of data can be modeled or measured easily using exponential and logarithmic functions. For example, consider ideal gases: Pressure versus volume give a curved plot, but a log graph of pressure versus volume provides a linear plot that is easier to interpret. Log

### Basic Functional Analysis

I've attached the problem I need assistance with. Thanks! Prove that A is convex and absorbing and....

### Unit Ball Basic Functional Analysis

Prove that the unit ball in a normed vector space is convex, balanced and absorbing set.

### Sketch a region with polar coordinates

Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions. 0 less than or equal to theta that is less than or equal to pie/3

### Find area of parallelogram

Find the area of the parallelogram with vertices A(0,1), B(3,0), C(5,-2), D(2,-1)

### Maximum likelihood estimator

Problem:What is the maximum likelihood estimator of the mean of x where x is the sample with distribution f(x)=rt^x where t= 1-r and r is between 0 and 1 and the mean of rt^x is t/r.

### Finding Work Done in a Force Field

1.)F(x,y)= (x^2)(y^3)i + (x^3)(y^2)j; P(0,0), Q(2,1).

### Determine whether the sequence converges or diverges.

Please see the attached file for the fully formatted problems.

### Spectral Theory, Functional Analysis, Operator Theory : Linear Operators, Bacach Space and Compact Operator

Please see the attached file for the fully formatted problems.

### Critical Numbers for a Function

What are all the possible critical numbers for f(x) = 4x^6 e^(5x)? See the attached file.

### 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

### Inverse Proportion

When the temperture stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 70 cubic inches of gas at a pressure of 14 pounds per square inch, find the new pressure of the of gas if the volume is decreased to 14 cubic inches. y is directly proportional to x

### Secant Lines - Tabulating Changes

Please see the attached file for the fully formatted problems. 1. Let . Tabulate the change of over the intervals (i) , (ii) , (iii) , (iv) , (v) . Graph together with the secant line passing through and .

### Removable Discontinuity

Where is the function f(x)={1/x^4 if x does not equal 0 {0 if x = 0 discontinuous? Is this a removable discontinuity?

### Maximum Value on an Interval

Find the absolute maximum value for f(x) = x^2 - 4x - 32 on the interval [-3, 9]. 8 11 13 14 18 24 30 none of these.

### Interval

Where on the interval [0, 2&#960;] is the function f (x) = x - sin x concave up? (&#960;=pi)

### Intervals

Please explain the steps and solution, thank you: Where on the interval [0, 2&#960;] is the function f (x) = x - sin x concave up? (&#960;=pi)

### Finding the Equation of a Parabola from its Focus

A satellite dish with a parabolic cross section is 6 feet in diameter. the receiver is located on the center axis, 1 foot from the base of the dish. How deep is the dish at its center?

### 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

### Surface Area of a Conic and Paramaterization in Cylindrical Coordinates

Please see the attached file for the fully formatted problems.