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Functional Analysis

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?

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.

Basic Functional Analysis

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

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

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.

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, 2π] is the function f (x) = x - sin x concave up? (π=pi)

Intervals

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

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

Density and Center of Mass

1) A plate is bounded by the curves y = -x^2, y = x^2, and x = 1. It has density d(x,y)=x. Make a sketch and find its center of mass. 2) A solid occupies a half-cylinder W: x^2 + y^2 is less than or equal to 4, y is greater than or equal to 0, z is greater than or equal to -3 and less than or equal to 3. It has constant