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Computing Values of Functions


Please see the attached file for the fully formatted problems. Problem 1 Consider the following two functions C&#57502; x &#57503;=&#8747;0 x cos&#57502;t2&#57503; dt S &#57502; x &#57503;=&#8747;0 x sin &#57502;t2&#57503; dt Write a program called <name>1.sce generates plots of these functions over the range 0&#8804;x&#

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

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).


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

[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

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

Substituting variable

Please show how to solve y'' - 3y^2=0, substituting v=y' so y'' = v dv/dy Initial conditions are y(0) =2 and y'(0)=4 I got it as far as dy/dx = (y^3 +c)^1/2 but that might be wrong!

Open Neighborhood of A

(See attached file for full problem description) If A is a nonempty set in a metric space X and if r>0 show that is an open neighborhood of A.

Closed set in a metric space

(See attached file for full problem description) If A is a closed set in a metric space (X,d) and , show that d(x,A)>0.

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

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?

System Response

Consider the following system in the attached file. Where Gc(s)= 10 for P controller = 10(1+1/s) for PI controller = 10(1+s+1/s) for PID controller Draw the response of the system for P, PI and PID controller using Simulink.

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

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.