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Calculus and Analysis

A solution of the 2d Laplace equation

Solve Laplace of u = 0 subject to the conditions: u(x,0) = f1(x) u(0,y) = 0 u(x,b) = 0 u(a,y) = 0 0<x<a 0<y<b (The question attachment contains a slightly different question. The question is restated correctly in the solution attachment)

Integrals

It is essential to show all steps by hand!! Also if a method is prescribed use only that method! 8)justifying its use, use L'Hospital's Rule to evaluate the following limit: lim ln(x^8) / 8x^8-8 x->1

Upper and lower control limits for /x- and R-charts

Find the upper and lower control limits for /x- and R-charts for the width of a chair seat when the sample grand mean (based on 30 samples of 6 observations each) is 27.0 inches, and the average range is 0.35 inches.

Graphing and Critical Points

2. Use calculus to sketch the graph of the function . Your sketch should address: a. An analysis of : it's domain, intercepts, and end behavior. b. An analysis of : the critical points, the extrema and classification, and each region of increase or decrease. c. An analysis of : the points of inflection, and the concavit

Second Order Ordinary Linear Differential Equations with Constant Coefficients

1). Given the differential equation for 1. L[y]= y''+2by'+b2y = exp(-bx)/x2, x>0 ; a) Find the complementary solution of (1) by solving L[y] = 0. b) Solve (1) by introducing the transformation y[x]= exp(-bx) v(x). into (1) and obtaining and solving completely a differential equation for v(x) . Now identify the part

Initial Value Problem

Which of the following is a solution of the given initial-value problem. y' + tan(x) y = 4 cos^2(x) y(0) = -4. on the interval -pi/2 < x < pi/2 A) y = 4 sin(x) - 4 cos(x) B) y = 4 cos(x) - 4 sin(x)cos(x) C) y = 4 sin(x)cos(x) + 4 cos(x) D) y = 4 sin(x)cos(x) - 4 cos(x) E) y = 4 sin(x) + 4

Writing Equations from Word Problems

Investments Morgan has $50,000 to invest and wants to receive $5000 interest the first year. He puts part in CD's earning 5.75%APY, part in bonds earning 8.75%APY and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growth fund? Mixing Acid Solu

First Order Differential Equations

1. In the following, represent the situation pictorially and deduce the governing 1st order differential equations and initial condition for the quantity in question. a) A tank, containing 300 gallons of pure water initially, is emptied out in the following fashion. A salt solution of concentration ½ lb of salt per gallon is

First Order Differential Equations and Values of Parameters

Please see the attached file for the fully formatted problems. 1. Given satisfying , ; &#960; ; find 2. Given such that , ; list all possible solutions. For which of these does ?; ? 3. Suppose for it is known that Where "a" is a parameter. Determine the value of this parameter which ensure the existence

Surface area, volume, and work

Find the area of the surface obtained when the graph of y = x2, 0 &#8804; x &#8804; 1, is rotated around the y-axis. Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis. A 100-ft length of steel chain weighing 15 lb/ft is hanging

A calculation that, given a latitude and longitude, can return a search radius

Looking for a calculation that given a latitude and longitude can return a search radius Here is the issue: I have a table of zip codes with their corresponding longitude and latitude values. For any given zip code, I need all of the zip codes in a 10 mile search radius. How would I set up the calculations to perform such a t

Differential Equations

1. Solve: x*(dy/dx) - y = 2(x^2) * y 2. General solution for: dy/dx = ((x^2) + 1)/(2 - y) then particular solution for y = 4, x = - 3

Laplace Transforms

Please see the attached file for the fully formatted problems. Find the inverse laplace transform of these Find the laplace transform of these Equate the coefficients for A,B and C

Solid of Revolution and Limits

Evaluate &#8747;(log3x / 2x) (dx) R is bounded below by the x-axis and above by the curve y = 2cosx, Figure 11.1. Find the volume of the solid generated by revolving R around the y-axis by the method of cylindrical shells 0(< or =) x(< or =) pi/2 Find limx&#8594;&#8734; ( 3x-2/3x+2 )^x

R is the region that lies between the curve

R is the region that lies between the curve (Figure 15.1) and the x-axis from x = -3 to x = -1. Find: (a) the area of R, (b) the volume of the solid generated by revolving R around the y-axis. (c) the volume of the solid generated by revolving R around the x-axis. y=1 / x^2+4x+5

Integrals, Differential Equations and Limits

Please see the attached file for the fully formatted problems. Question 1 Find &#8747; x3+4 ________________________________________x2 dx Question 2 Solve the initial value problem: dy ________________________________________dx = x^/¯(9+x2) ; y(-4) = 0 Question 3 Figure 3.1 f(x) = x2+3 Figure 3.2

Roots, rate of change, and maximum and minimum

Find the maximum and minimum values attained by the function on the interval [0, 2]. h(x)=x-1/x+1 The equation has three distinct real roots. Approximate their locations by evaluating f at -2, -1, 0, 1, and 2. Then use Newton's method to approximate each of the three roots to four-place accuracy f(x)= x^3- 3x+ 1

Rotating a System

Write the equation in terms of a rotated x'y'-system using q, the angle of rotation. Write the equation involving x' and y' in standard form. x2 + 2xy + y2 - 8x + 8y = 0; q = 45° x'2 = -4sqrt2y'2 x'2 = -4sprt2y' 3x'2 - 4sqrt2x'y' + y'2 = 0 2x'2 - sqrt2x'y' + 2y'2 = 0

Minimizing Perimeter of a Fence and Finding the Nearest Point on a Line

1. A rancher wishes to fence in a rectangular corral enclosing 1300 sq yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible. 2. Find t