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Computing Values of Functions

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!

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?

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)

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

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?

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.

Working with iterative methods.

The sequence of value given by the iterative formula is X n+1=2/9-lnXn with initial value X=1,converges to alpha. 1) State an equation satisfied by alpha, and hence show that alpha is the x coordinate of a point on the curve where y=3. 2) Use this iterative formula to find alpha correct to 2 decimal places, showin

The one norm

Prove rigorously that ||x + y||1 <= ||x||1 + ||y||1

Function

A function f is defined on a set of real numbers. Is f one-to-one? Please give explanation so I may understand. (see attached file for function)

Linearization of a function. Attachments in Word.

The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras' theorem by the expression: (Please see the attachment below) (a) Find an expression which serves as a linear approximation for l at h=1000 m. (b) Give two assumptions you think have been made in deriving