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Computing Values of Functions

One to One and Inverse Functions

Let A = {1,2,3} and B = {a,b,c}, and let f: A B. (a) Give an example of a one to one function from A to B (use the given sets A and B above). Briefly explain why your example is a 1-1 (one-to-one) function. (b) How many one to one functions from A to B are there? Explain. (c) Using the above sets A and B define a fu

Modeling a Box as a Particle

See attached file for full problem description. Need help on 2b, 3. 2. A box of mass m is placed on a plane, which is inclined at an angle a to the horizontal, where tan a The plane is rough and the coefficient of friction between the box and the plane is . The box is kept in equilibrium on the plane by applying a horizontal

Banach Spaces

Show that (X, ||*||) is a Banach space if and only if {x in X: ||x||=1} is complete. Know that in the first direction, we must show that {x in X: ||x||=1} is closed subset of X. For the reverse direction, I know I have to take a cauchy sequence and translate it to the unit circle and then show that if it is convergent ther

Functions and Sequences of Iterates

Let f be a function defined on [a,b] and suppose that z is a point in (a,b) such that f(z) = z. Further suppose that there is a number alpha < 1 such that f ' (x) < alpha for all x contained in (a,b) and that 0 < f ' (x) for all x contained in (a, b). a.) Prove that if z<x, then z<f(x) and that f(x) - z < alpha(x-z).

Absolute and Relative Errors : Three-Digit Chopping and Rounding Arithmetic

Please help with the following problems. Provide step by step calculations. Compute the absolute error and the relative error in approximations of p by p*. a) p = pi , p* = 22/7 Perform the the following computations i) exactly, ii) using three-digit chopping arithmetic, iii) using three digit rounding arithmetic. iv) Com

Predicates, Logical Connectives and Quantifiers

Let P(x), Q(x) and R(x) be statements "x is a clear explanation", "x is satisfactory" and "x is an excuse" respectively. Suppose that the universe of discourse for x consists of all English test. Express the following statements using quantifiers, logical connectives and P(x), Q(x) and R(x) a) All clear explanations are satis

Is the packing process capable? Is an adjustment needed?

Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weight of 12 ounces (340grams) per box. Each box contains eight individual 1.5 ounce packets. To reduce the chances of shorting the customer, product design specifications call for the packet-filling process average to be set at 43.5 grams. Tolerances ar

Inverse functions: True or false questions

True or false. Determine whether the statement is true or false. If false, explain why and give an example that shows its false. 1) If the inverse function of f exists, then the y-intercept of f is an x-intercept of f^-1 (f inverse). 2) There exists no function f such that f = f^-1 (f inverse)

Increasing Functions

Which of the functions below is increasing for all x-values? f(x) = x - 7 f(x) = x2 - 7 f(x) = x3 - 7 f(x) = x4 - 7

Metric Spaces

(See attached file for full problem description) 1. Show that the functions d defined below satisfy the properties of a metric. a. Let X be any nonempty set and let d be defined by The d is the call the discrete metric. b. If X is the set of all m-tuples of real numbers and, if for and , then (X,d) is a metric spac

Use Matlab to calculate correlation between heartbeat record

Load ECG data from exercise 1 into MATLAB. Select a segment of recording encompassing at least 10 cycles of the heartbeat. Use Matlab to coherently average 10 cycles to produce a plot of one full cardiac cycle with an improved signal-to-noise ratio. Include plots of the average cycle with labeled axis. Use Matlab to calculat

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=&#8730;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 &#945; i

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.

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

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!


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?