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# Computing Values of Functions

### Greatest Common Factors

Find the GCF: (12,18), (16,20) (44,153) I tried to do on my own, I'm not sure if I understand what I am doing. If you can would it be possible to describe in details exactly what I should be doing. Thanks.

### Proving Differentiability

Please see the attached file for the fully formatted problems. 2. Suppose that f, g, h are three functions defined on (a, b) and c (a, b). Assume that f and h are differentiable at c, f(c) = h(c), and f(x) g(x) h(x) for all x (a, b). Prove that g is also differentiable at c and (c) = (c) = (c).

### Population Growth Problems

In a galaxy far, far away (my professor writes his own practice problems), on the planet Xylor, a herd of 100 Tybars was introduced for breeding. After 5 years, the herd had increased to 500. If the rate of herd growth is assumed to be directly proportional to the number of Tybars present on Xylor at any time t: a. How many T

### Green's Functions, Parabolic Equations and Heat Equation

I am having great difficulty understanding how you derive Green's functions, particularly how the boundary conditions are incorporated. I've also not studied Fourier series before and it appears that these are also used particularly in developing solutions for parabolic PDEs. My text does not have any specific worked examples

### Proof: Bijective, One-to-one and Onto Functions

1. Consider f:A->A a one-to-one function. Prove that f is also onto. 2. Consider f:A->A an onto function. Prove that f is also one-to-one. A is a finite set. Hint: whenever we have a finite set it is often useful to actually enumerate its elements, i.e. A={a1,a2,....,an}

### Functions and their graphs

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2008. Show how each

### Second-order and Third-order Rational Functions

Task Name: Phase 3 Discussion Board Deliverable Length: 2-4 paragraphs Details: One of the advantages of rational functions is that even rational functions with low-order polynomials can provide excellent fits to complex experimental data. Linear-to-linear rational functions have been used to describe earthquake plates. As a

### Second and Third Order Rational Functions

To explore the versatility of rational functions, choose a second-order/third-order (e.g., x2/x3) and a third-order/second-order (e.g., x3/x2) rational function. Provide a graph for the second-order rational function (e.g., x2), choosing x values in the range from -10 through +10. Then, provide at least three variations of th

### Solving an Estimation Problem

Short Response: You are mailing 19 packages. It costs between \$9 and \$12 to mail each package. Estimate the total cost. Explain the method.

### Estimate of Writing and Reading

Writing: You want to know whether 5 hours is enough time to read a book for class. To be sure you finish, should your estimate of the number of pages you can read per hour be high or low? Explain the reasoning.

### Estimation Methods in Mathematics

Describe the method used to estimate the sum, difference, product, or quotient. Then describe a better method and revise the estimate. 1) 362 - 118 &#8776; 400 - 100 = 300 2) 19 x 2 &#8776; 20 x 0 = 0 3) 148 + 138 &#8776; 100 + 100 = 200 4) 305 ÷ 16 &#8776; 300 ÷ 20 = 15

### SciLab

Please see the attached file for the fully formatted problems. Problem 1 Consider the following two functions (see the attached file). Write a program called <name>1.sce generates plots of these functions over the range 0&#8804;x&#8804;8 on a single figure. Format the figure so that it is very readable and visually appealing

### Heat Equations, Gram-Schmidt Orthogonalization and Nonuniform Membranes

See attached file for full problem description. You can solve problems except matlab problems(1.(c),3(c),6(d,e)). But I still hope you would solve all problems including matlab problems. And you can send me solutions separating into two parts regardless of problem's order.

### Sequences and Series: Using the index of a series as the domain and the value of the series as the range, is a series a function?

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadrati

### Possible Values of a Random Variable

Assume that the box contains balls numbered from 1 through 22, and that 3 are selected. A random variable x is defined as 3 times the number of odd balls selected, plus 4 times the number of even. How many different values are possible for the random variable x?

### Average Value of a Function and Length of Path

1) Find the average value of the function f(x, y, z) = 1/(x^2 + y^2 + z^2) over the region where x^2 + y^2 + z^2 is greater than or equal to 1 and less than or equal to 4. 2) Find the length of the path in R^2 that in polar coordinates r, theta is given by r(t) = 2t, theta(t) = t, and t is greater than or equal to 0 and les

### Meromorphic Functions

Show that any function which meromorphic in the extended plane is rational.

### 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

### Maxima and Minima of Functions

Find the maxima and minima of the following functions on the indicated intervals: a. f(x) = x^3 - 7x + 6 on the interval [0,4]. b. f(x) = sinx + 2cosx on the interval [0, 2(pi)]

### Solve: Odd, Even, or Neither Functions

Determine whether each of the following functions is odd, even or neither. a. f(x) = 3x^2 + 4x^3 b. f(x) = 5x^-2 - 4x^4 c. f(x) = x^3 - x Show all work.

### Block Diagrams : Mason's Gain Formula and Transfer Functions

Please solve attached 2 questions using Mason's Rule. See attached file for full problem description. keywords: masons rule

### 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).

### Differentiability of functions

Discuss the differentiability of each of the following functions at all real numbers and find its derivative at those real numbers at which it is differentiable. See attached file for full problem description.

### 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

### Deriving Equations Expressed

[EQUATION] PVx = C can be expressed as p1v1 = p2v2 and combine this with the ideal gas law pv=RT to obtain the [EQUATION] above. Derive the top equation. Please see the attached file for the fully formatted problems.

### 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)