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    Calculus and Analysis

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    Taylor Series Expansion: Differential Equations

    See attached. Determine the Taylor series expansion of the function... Use a power series method to find the complete solution of.... find two linearly independent solutions of the differential equation.... For the Bessel equation of order zero...

    Laplace Transform and Initial Value Problems

    (See attached for full description). 1. Find the Laplace transforms of 2. Use the Laplace transforms to solve the initial value problem y'' + 2y' - 8y = 0, y(0) = 1, y'(0) = 8 3. Solve the initial value problem y'' + 2y = r(t), y(0) = y'(0) = 0 Where r(t) = 1 for 0 <t <1 and r(t) =0 otherwise 4. Solve the initial

    When two chemicals A and B react to form C and a byproduct.

    (See attachment for detailed description) When two chemicals A and B react, 1g of A and 2g of B yield 2g of C and a byproduct. The rate at which C is formed is proportional to the amount of A and B present. Suppose that at the outset there are 50g of A and 90g of B present, and that after 1 hour, 45g of C have been formed.

    Calculus - Exponential Distribution

    The following table gives the percent of the US Population living in urban Areas as a function of year2. ... 5. (a) Estimate f'(2) using the values of f in the table. ... 5. The thickness, P, in mm, of pelican eggshell depends ... 11. The quantity, Q mg, of nicotine in the body t minutes after a cigarette is smoked ... [Pl

    Calculus to find volume

    1. direction: Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y=2/x, y=-x+3 ( note: the 2 is over a fraction bar and the x is the denominator) 2. Solve the problem. An auxiliary fuel tank for a helicopter is shaped l

    Differential equation

    7) solve the differential equation y' = 6(y-1)^3(4x+3)^2, isolating y - that is, by writing the solution as y as a function of x

    Polar Graphing

    sketch a graph of r = sin (2theta), 0<=theta<=2pi, and calculate the area of one petal, rounding to the nearest hundredth

    Writing parametric equations

    2)Write a set of parametric equations for each of the following figures. (i) the line segment with endpoints at (3,-5) and (-2,11), such that the parameter value t satisfies 0<=t<=1. (ii)the lower half of the circle with center (-7,8) and radius 9

    Series and Sequences of Parametric Equations

    Following are the instructions from my teacher for the final review. please follow directions precisely and show all steps by hand. Answers must be exact unless otherwise indicated. 1) Consider the parametric equations x =2t+1/t and y = 1-t. (i) Using a table sketch the curve represented by the parametric equations. Writ

    Elementary Differential Equations

    Please show the steps in the attached problems so that I can better understand what I am learning. Q1 is a Bernoulli equation, primes denote derivatives with respect to x. Please only complete questions 1 and 2. 1. Find the general solution to 2xy' + y^3 * exp(-2x) = 2xy. 2. Find the general solution of reducible sec

    Provide a plot of temperature versus distance east.

    Linear equation that relates Celsius to Fahrenheit : Your company was very impressed with your results from the recent study. They have asked that you investigate another location for them and present this new promising location at the upcoming sales meeting. Again, it is your job to check out the various areas and the frien

    Model the Data for Temperature of Water and the Heat Supplied

    Water is the most important substance on Earth. One reason for its usefulness is that it exists as a liquid over a wide range of temperatures. In its liquid range water absorbs or releases heat directly in proportion ot its change in temperature. Consider the following data that shows temperature of a 1,000 g sample of water at

    Taylor expansion

    Dear OTA, Please help me in solving the attached problem. Thanks

    ACME Construction Company is building a suspension bridge over the Miami River. They need to know how much material will be required to construct the main support cables and what sort of cable they need to buy. The support cables will be attached at either end to the top of 100 meter tall concrete pillars. The two concrete pillars are 200 meters apart. The cable should hang down 50 meters at its lowest point. Gottfried Leibniz and Christian Huygens in 1691 determined that any cable hanging under the force of gravity must have the shape of the graph This shape is known as a catenary. The parameter "a" is the ratio of cable tension to cable density and . The only use of the parameter b is to provide a vertical shift, if necessary. ACME would like to hire your group to find two things for them. First, what values must a and b have in order for the catenary to fit the constraints imposed by the placement of the concrete pillars and the low point of the cable? They are especially interested in the parameter a since this tells them what tension the cable will be under. Second, what length cable do they need? You should try to give a formula for the cable length in terms of the cable function y(x). That way, ACME can use your result for other cable shapes as well. Following are several hints for solving this problem. When you write your report for ACME, you must explain to them, step by step, how you solved the problems. You will need to use a combination of graphs, equations and text. You must try to convince them that your results are correct. It's no use to them if they have to solve the problem themselves in order to verify your results.

    ACME Construction Company is building a suspension bridge over the Miami River. They need to know how much material will be required to construct the main support cables and what sort of cable they need to buy. The support cables will be attached at either end to the top of 100 meter tall concrete pillars. The two concrete pilla

    Fubini theorem integrals

    Triple Integral using Fubini Theorem: Evaluate ∭_E▒e^x dV E ={(x,y,z):0≤ y ≤ 1,0≤ x ≤y,0 ≤ z ≤ x+y}