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# Computing Values of Functions

### 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.

Suppose the number of beers you drink depends on the number of football games you watch. If you drink five beers during every football game, the function would be Number of Beers (B)=5 times Number of Football Games (F), or B=5F. Write a brief describing this function that comes from your own life. It could be something about th

### Weierstrass Approximation Theroem

Note: abs = absolute value Define f(x) = abs(x - 1/2) for 0 <=x <= 1. Use the proof of the Approximation Theorem to find an explicit polynomial p:R->R such that abs(f(x) - p(x)) < 1/4 for all x in [0,1]

### Weierstrass Approximation Theorem

This question is about the Weierstrass Approximation Theorem Show that the Approximation Theorem does not hold if we replace I by R(real number system), by showing that if f(x) = e^x for all x, then f:R->R cannot be uniformly approximated by polynomials.

### D'Alembert's formula

Utt means the second derivative with respect to t Uxx means the second derivative with respect to x Utt = 4Uxx, -(inf) < x < (inf), t > 0 U(x,0) = x, Ut(x,0) = xe^(-x^2) for -(inf) < x < (inf) Please use D'Alembert's Formula and show all work. If there is Fourier series, please show how you got eigenvalues and eige

### Iteration Formula Sequence

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

### Finding the values of the sides of a parallelogram.

Find the value of each variable in the parallelogram. 2z+1 4w 4z-5 w+3

### The one norm

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

### One-To-One Functions Determined

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)

### Four stationary points of a multivariable function

A surface is described by the multivariable function f(x,y) where: f(x,y) = x^3 + y^3 + 9(x^2 + y^2) + 12xy a) Show that the four stationary points of this function are located at: (x1, y1) = (0, 0) (x2, y2) = (-10, -10) (x3, y3) = (-4, 2) (x4, y4) = (2, -4)

### 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