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    Calculus and Analysis

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    Work in a force field

    Please see the attached pdf. Consider the force field ....Compute the work done in a moving particle along the parabola

    Fundamental theorem of calculus found

    See attachment Use Part I of the fundamental theorem of calculus to find the derivative of the function... The velocity graph of an accelerating car is shown... Find the interval on which the curve....is concave upward

    Example of Finding an Image

    Section 6.1 The Geometry of Maps from R^2 to R^2. Please see the attached pdf. file. Let D*=[0,1]x[0,1] and define T on D* by T(u,v)=(-u^2+4u,v). Find the image of D. Is T one-to-one?

    Bessel functions and Legendre polynomials

    1).The Bessel functions Jp satisfy the equations (see attached file) . Use this to show that Bessel functions satisfy Bessel's differential equation. 2) The legendre polynomials satisfy... (see attached) where Pn(x) is the Legendre polynomial of degree n. Show that the Legendre satisfy Legendre's differential equation, (see atta

    Rate of change

    See attachment Section 11.3 1) The quarterly profit of Cunningham Realty depends on the amount of money x spent on advertising/quarter according to the rule: where and x are measured in thousands of dollars. What is Cunningham's profit when its quarterly advertising budget is $35,000.00? 2) Suppose

    Inverse Laplace Transformation and Partial Fraction Expansion

    Please help me with these problems. section 7.4 6,16,20,24 Samples of these questions appear below. Please see the attached files for the fully formatted problems. Find the inverse Laplace transformation. Determine Partial Fraction Expansions for the given rational function. Determine L^-1{F}.

    Laplace transform

    Hi, Please help on these problems Please show all steps Section 7.3 # 4,8,14,20 See attached determine the Laplace transform of the given function.

    Working with Differential Equations: Word Problems

    Please show all steps. section 6.4 # 2,4,6,14 section 7.2 #4,12,18,31 See attached. Use the method of variation of parameters... Determine the Laplace transform.... use the Laplace transform table and the linearity of the Laplace transform to determine the following transforms...

    General solution for differential equations

    Hi, Please help Please show all steps section 6.3 #4,8,24,28 see attached Use the method of undetermined coefficients... Find a general solution... Use the annihilator method...

    Differential Equation and General Solutions

    Please help on these problems, please list out all steps. section 6.2 # 4,10,14,18,22 See attached Find a general solution for the differential equation with x as the independent variable. Find a general solution to the given homogeneous equation. Find a general solution for the given linear system using the eliminati

    Step Function and Laplace Transform

    Please show all steps to solution. Sketch the step-function f(t) = 1, 0 < t < 1 2,1 < t < 2 1,2 < t < 3 0,3 < t < &#8734; Rewrite this function in terms of the unit-step function ,and compute the Laplace transform of f.Simplify you

    Inverse of Laplace Transform

    Please see the attached file for the fully formatted problems. Find the inverse Laplace transform of the function F(s) =[(s+2)e^s]/[(s+2)^2 + 9] You may use a short table of Laplace transform. Show all of the steps necessary for calculation.

    Laplace transforms

    Please show all steps to solution. Apply the method of Laplace transforms to solve the initial-value problem y'+y=e^t , where y(0)=0

    Inverse Laplace Transform

    Please see the attached file for the fully formatted problem. Find the inverse Laplace transform of the function: F(s) = 2e^(-3s)/s - e^(-s)/s You may use a table of Laplace transforms. Show all of the steps necessary for this calculation.

    Business calculus

    Problem attached Revenue: A company sells a seasonal product. The revenue R (in dollars per year) generate by sales of the product can be modeled by: R = 410.5t^(2)e^(-t/30) +25,000 0 < t < 365 where t represents the day (a) Find the average daily revenue during the first quarter which is given by 0 < t < 90 (b) Find t

    Average Daily Revenue of the Seasonal Product

    Problem attached Revenue: A company sells a seasonal product that generates a daily revenue R (in dollars per year) modeled by: R = 0.06t^2 (365 - t)^1/2 + 1250 0 < t < 365 where t represents the day (a) Find the average daily revenue over a period of one year (b) Describe a seasonal product whose seasonal sales pattern re

    Solving an IVP using Laplace Transform

    Please see the attached file for the fully formatted problem. Apply the method of Laplace transforms to solve the initial-value problem y'' - y = u1(t) where y(0) = 0 and y'(0) = 0.

    Initial value

    Please show all steps to solution. Apply the method of Laplace transforms to solve the initial-value problem ...

    Business Calculus: Revenue

    Please help with the following questions regarding calculus and analysis. Revenue: Two models, R1 and R2, are given for the revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2004-2008, with t = 4 corresponding to the year 2004. Which model is projecting the

    Area of a region

    Sketch the region between the graphs of the functions and compute the area of this region. y = 1/x, y = x^3, x = 1/2, x = 1.

    Business Calculus re: Mortgage Debt

    Mortgage Debt. The rate of change of mortgage debt outstanding for one to four family homes in the United States from 1993 to 2002 can be modeled by: dM/dt = 5.4399t^2 + 6603.7e^-t where M is the mortgage debt outstanding (in billions of dollars) and t = 3 corresponds to 1993. In 1993, the outstanding mortgage in the US was