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Computing Values of Functions

Manufacturing Costs and Cost Functions

Manufacturing Cost The weekly production cost C (in dollars) of manufacturing x hand calculators is given by the formula C = 6000 + 8x - x 2 / 1000. What is the cost of producing 1000 hand calculators?

Is the square root of x2=x an identity (true for all values of x)?

Is the square root of x2=x an identity (true for all values of x)? For the equation x-squarex=0 perform the following a. solve for all values of x that satisfies the equation. b. graph the function y=x and y=√x on the same graph (by plotting points if necessary). Show the points of intersection of these two graph

PID Controller : Ziegler-Nichols Tuning Method

Consider the following system shown in Fig.2 (attached file) in which a PID controller is used to control the system. The PID controller has the transfer function Gc(s) = Kp(1 + 1/Tis + Tds) Design a PID controller for this system using Ziegler-Nichols tuning method for determination of Kp, Ti and Td. Then obtain a unit-

Bessel Functions and Sturm-Liouville Problem

(See attached file for full problem description) --- Use the following table to solve 3 and 4. J0(x) J1(x) Y0(x) Y1(x) 2.4048 0.0000 0.8936 2.1971 5.5201 3.8317 3.9577 5.4297 8.6537 7.0156 7.0861 8.5960 11.7915 10.1735 10.2223 11.7492 14.9309 13.3237 13.3611 14.8974 3. Find the first four α i

Uniqueness of a Reflector

Show that if Qx=y, where Q= I- ruu^T (r can be denoted as gamma) , then u must be a multiple of x-y. In other words, prove the uniqueness of reflector Q.

Consider the Initial Value Problem

Consider the initial value problem on [1,2]: x^2*y'' + xy' - K^2*y = 0, y(1) =1, y'(1)=0 Find the solution y(x,K). Is it a continuous function of K? Can it be differentiated with respect to K? K is a constant. See the attached file.

Relations and Functions: Domain and Range

Determine each of the following based on the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}. 1. Is the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)} a function? 2. Identify the domain of the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}. 3. Identify the range of the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}.

Unit-Step Response using MATLAB

Using MATLAB, obtain the unit-step response of the following system: C(s)/R(s) = 10/s^2 +2s + 10 where R(s) and C(s) are Laplace transforms of the input r(t) and output c(t), respectively. Hint: Use the following command; step(num,den)

Define the function A

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) --- 12.6-3 Let be a complete orthogonal family in . Define the function A from into .( This means: In order to manufacture our metric space we must therefore regard any two function whose valu

Bessel Function, proofs

USING THE BESSEL FUNCTION OF ORDER ZERO: Verify that it is the solution to the differential equation x^2 y'' + x y' + _x^2 y = 0, satisfying y(0)=1, y'(0)=0. Here y' means the first derivative of y(x) and y'' means the second derivative.

Harmonic and Analytic Function

Give an example (and explain why it works) of an analytic function u on a harmonic function v such that the composite function u o v is defined but NOT harmonic. Please see the attached file for the fully formatted problem.

Use the values for approximation to M.

(See attached file for full problem description with proper equations and exponents) --- 1. Suppose that N(h) is an approximation to M for every h > 0 and that M = N(h)+K1h2+K2h4+K3h6+..... For some value K1, K2, K3... Use the values N(h), N(h/3), and N(h/9) to produce an O(h6) approximation to M. ---

Definitions : Sequence, Geometric Progression, String, Recursive

On the following terms could you please give my an English text description - in your own words. Thanks. 1. Sequence 2. Geometric Progression 3. String 4. Recursive definition of a function 5. Recursive definition of a set 6. Recursive algorithm 7. Program correctness 8. Loop invariant 9. Final assertion

Trouble with Bolzano-Weierstrauss

This involves the Bolzano-Weierstrauss Theorem, I believe, but I'm not sure where to start. Prove that the set of open disks in the xy plane with center (x,x) and radius x > 0, x rational, is a countable covering of the set {(x,y): x > 0, y > 0}

Solve for X and Solving a Quartic Function

Solve 1. X + 3 - X+ 4 = X + 5 - X + 6 X + 2 X + 3 X + 4 X + 5 2. Higher education French language registration in the USA from 1970 to 1998 can be modeled with the quartic function f(x) = 0.004X - 0.2268X + 5.836X - 46.121X + 360.046, where f is in thousands and x is the number of years since 1970. Use th

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

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!