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# Computing Values of Functions

### Cost Function : Average Cost, Revenue and Profit - Maximum or Minimum

Given the cost function C(q) = 4000 + 50q + 0.002q2 and the demand function p = 80 - 0.025q, find the value of q for which: (a) Average cost is a minimum. (b) Revenue is a maximum. (c) Profit is a maximum. ---

### Fixed Point of Function & Matlab Program for the Newton-Raphson

1. Let g: R&#8594;R+ be such a function that g&#8712; C^1(R) and for all x &#8712; R, -1 <g'(x) < 0. Show that the sequence Xn+1 : = g(Xn) converges to the unique fixed point of the function g, regardless of chioce Xo &#8712; R. [ Note : Observe that the domain of function g is not a compact interval.] 2. Write a matla

### Local or Uniform Lipschitz Constants

Determine if the following functions satisfy local or uniform Lipschitz condition. 1). te^y My work: I found d/dy (te^y) = te^y, and this is not bounded above for any value of y, so this made me conclude that it has locally Lipschitz condition since the Lipschitz constant here changes as the reagion changes? Am I right?

### Closed Locker Problem

School is about to begin. The janitor has all the lockers closed. All 1000 of them. Student #1 comes along and opens ALL of the lockers. Student #2 comes along and closes doors 2, 4, 6, 8, 10, etc.... Student #3 comes along and changes the state of every 3rd locker ( 3, 6, 9, 12, 15). Student #4 comes along and c

### Continuous function proof

Let f:rxr-->r be defined by the equation.... --- (See attached file for full problem description)

### Necessary and sufficient condition for a Jacobian to be zero

Real Analysis Jacobians(I) Necessary and sufficient condition for the value of a Jacobian of n independent functions to be zero The fully formatted problem is in the attached file.

### Dirichelet problem

I need to use separation of variables to solve Laplace's equation in the annular sector: 1< r<2, 0< theta< pi/2, u(1,theta)= f(theta), u(2,theta)=0, u(r,0)=0, u(r,pi/2)=0 Thank you!

### Statistics

The average numbers of home runs hit by the Boston Red Sox per game are: 2 divided by 3 = .66 5 divided by 2 = 2.5 6 divided by 1 = 6 7 divided by 0 = 0 Is that correct using the weighted approach?

### Harmonic Function: Analyticity, Compactness and Minimum Value

Let (attached) be a function that is analytic and not constant throughtout a bounded domain (attached) and continuous (attached) on its boundary (here domain is an open connected set). Prove, by considering (attached) , that the component function (attached) has a minimum value in the compact region (attached) which occurs on

### Functions and Graphs

Having trouble researching the number of deaths in the US each year due to each of the following medical conditions in each of these years: 1985, 1990, 1995, and 2002. heart disease, cancer and aids e.g. The websites keep bringing up different types of cancer, nothing is specific. Totally frustrated... e.g. 1980 throug

### Jacobi and Gauss-Seidel iteration

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Thank you. Start with P0 = 0 and use Jacobi iteration to find..... (Complete problem found in attachment)

### Gradient of the quotient of two scalar point functions. If f and g are two scalar point functions, then grad (f/g) = ( g grad f - f grad g )/g^2, that is, gradient of (f/g) = ( g gradient of f - f gradient of g )/g^2, that is, (f/g) = (g f - f g)/g^2

Important Formulas and their Explanations (V): Gradient, Divergence and Curl Gradient of the quotient of two scalar point functions

### Problem involving Differential Equations

A mass 5kg is attached to a spring suspended from the ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 2m. The mass... Determine the motion of the mass. Decribe its motion in as much detail as possible. Please see attached.

### Composition of Values of Functions

(g o f) (1) let f(x)= 2x-3, g(x)= x2 + 3.

### Demand Function, Cost Function. When x=500 units, is the demand elastic, inelastic, or unit elastic? Determine the production level of x that will minimize the average cost for this product. What is the average cost at this production level? What is the cost at this production level?

1. When x=500 units, is the demand elastic, inelastic, or unit elastic? The demand function is P(x) = 100-x/400 in dollars 2. The cost function to produce x items is given by: C(x)=1/9x^2 - 2x + 100 in dollars. Determine the production level of x that will minimize the average cost for this product. What is the ave

### Knapsack Problem : Write in Canonical Form

Let [EQUATION1] with [EQUATION2] and [EQUATION3]. The idea is to write each such set in some simple canonical form. (i) When n = 2, how many distinct knapsack sets are there? Write them out in a canonical form with integral coefficients and 1 = [EQUATION4]. (ii) Repeat for n = 3 with [EQUATION5]. *(For proper equations an

### Continuous functions on closed intervals

See attached, ps explain correct answer Let f be a function that is continuous on the closed interval [0,1] and differentiable on the open interval (0,1). If f(0) = f(1), then which of the following statements must be true? A. f has a minimum at some x0 such that 0 < x0 < 1. B. f has a maximum at some x0 such that 0 < x0

### 3-Regular Polyhedron: How many square faces can the polyhedron have?

5. The faces of a 3-regular polyhedron are all squares or hexagons. How many square faces can the polyhedron have? Does the number of square faces uniquely determine the polyhedron? (Please see attachment)

### Periodic function proof

Please provide explanation to prove that f(x)=sin(x)+sin(x/sqrt(2)) is not periodic.

### Carrying capacity

Suppose that a population develops according to the logistic equation: dP/dt = 0.15P - 0.003P^2 where t is measured in weeks. what is the carrying capacity?

### Logistic model

A population obeys the logistic model. It satisfies the equation : dP/dt = 2/1300 P(13-P) for P>0 Find when P is increasing and decreasing.

### Obtaining a Target Number

Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (You have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.

### Composition of Cycles Functions

Find the composition of the following cycles representing permutations on A = {1,2,3,4,5,6,7,8} Answer as a composition of one or more disjoint cycles. A) (1,3,4) . (5,1,2) B) (2,7,8) . (1,2,4,6,8) C) (1,3,4) . (5,6) . (2,3,5) . (6,1)

### Exponential Order Application

Show that a) e^(t^2) is not of exponential order, and b) e^(t^1/2) is of exponential order

### Pursuit Example Problem

A dog walks north from a crossroads at 1 mile per hour. The dog's master begins one mile east of the crossroads and walks at all times directly at the dog with a speed of s>1 miles per hour. 1. Find the equation (in the form y = f(x)) that describes the path of the master. 2. When and where does the master overtake the do

### Function of a Function: Find (gof)(x)

See attachment Given f(x) = sqrt(x^2) -1 g(x) = 2/x Find (gof)(x).

### Function Situation Mailing Packages

Postal Restrictions If a box with square cross section is to be sent by the postal service, there are restrictions on its size such that its Volume is given by V= x²(108-4x), where x is the length of each side of the cross section (in inches). (a) Is V a function of x? (b) If V= V(x), find V(10) and V(20). (c) What restr

### Relationship Between Feasible Potentials and Negative Dicycles

Let G be a directed graph where c_e is the cost of arc e. If the nodes of G can be assigned feasible potentials then G has no negative dicycle.