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    Calculus and Analysis

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    Present Value of Money and Calculus

    Please answer the following questions: The Present value of money is the amount that you need to deposit now in order to have a desired amount sometime in the future . 1. What is the present value needed in order to have saved $60,000 in five years, given an annual interest rate of 7% compounded monthly? 2. What is the

    Volume of revolution..

    Consider the function x=12(y^2-y^3). Determine why revolving this curve about the x-axis has a different volume than revolving about a line y=1.

    Differential Equations : Equations of Motion, Laplace Transforms

    Refer to figure 2 in attachment. a) Write the equations of motion for the mechanical system.****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) Take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the co

    Length of a curve

    Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: x=(y³∕6) + 1/(2y) from y=2 to y=3 Hint: 1 + (dx/dy)². is a perfect square

    Identity Functions Detailed

    Prove the given identity - Please explain in detail. 14. 2 cos x - 2 cos^3x = sin x sin 2x 16. cos (x-y)/cos x cosy = 1 tan x tany 20. sec x -cos x = sin x tanx 22. sin 2x = 1/tanx +cot 2x 23. If tan x = 5/12 and sin x>0 , find sin 2x 26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pi

    Finding the Volume of Revolution Using the Shell Method

    Using the shell method, find the volume of a solid generated by revolving about the y axis. The boundaries of the solid are: y=9x/&#8730;(x³+9) the x-axis the line x=3 Note: I received a solution to this problem from an OTA, but it appeared that the integration wasn't complete. I would like to see another OTA sol

    Inverse Laplace Transforms and Convolution Integral

    Find the inverse Laplace transform of the following: (a) 10/(s2+9) (b) 2e^-2s /(s+3) (c) .... (d) Find the inverse Laplace transform of F(s) using convolution integral where F(s) = .... Please see the attached file for the fully formatted problems.

    Limits and L'Hopital's Rule (34 Problems with High Quality Solutions)

    Find the limits using L'Hopital's rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's rule does not apply explain why. 1) lim as x approaches -1 (x^2 -1) / (x + 1) 2) lim as x approaches -1 (x^9 -1) / (x^5 - 1) 3) lim as x approaches -2 (x+2) / (x^2 +3x + 2) 4) lim as x approa

    Graphing, Translation, Reflection, Domains, Limits, Derivatives

    For the following graph the given functions on a computer screen, how are these graphs related? 1) Y=2^x, y=e^x, y=5^x, y=20^x 2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x _______________________________________________________________________ Make a sketch of the function. 7) y=4^x-3 8) y=-2x^-x 9) y=3-e^x 13)

    Inverse function Values

    Please solve each problem with a detailed solution showing each step to solve the problem. Since the symbols confuse me at times please use "baby" math to show how to get from the start to the end. I understand the book in some ways, but the more I see completed the better I can think about the rest of the problems I need to d

    Differential Equations : Show that the differential equation

    Show that the differential equation is not exact. It can be made exact by multiplying throughout by , where m and n are integers. Find m and n and hence, or otherwise, solve the equation. Please see the attached file for the fully formatted problems.

    Solutions to various differential equations

    Please find the attachment for the questions. Five Linear Homogeneous Differential equations that are to be solved using Variables separable and other standard methods are given in the attachment

    Cauchy principal value, residue

    Verify the integral formula with the aid of residues. 1.) Show that the p.v. of the integral of (x^2+1)/(x^4+1) from 0 to infinite = (pi)/(sqrt 2). Note: p.v.=principal value; pi is approximately 3.14; sqrt 2=square root of 2 Please show all work and explain the steps, especially how you found the zeros of the

    LaPlace transformation functions

    Could some one please help me with the problem and provide all the steps. y'' + y = SQRT2 * Sin (tSQRT2) with y(0) = 10 and y' (0) = 0