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Calculus and Analysis

Stochastic Differential Equations, Density Functions and Random Variables

We use the notation X ~N(μ, σ2) to indicate that the density function for the continuous random variable X, fx(x), has the form .... (a) If X ~N(μ, σ2) show that..... (Hint: you will need to know how to find the density function for X ? μ from the density function for X). (b) If ...., and X1 and X2 a

Sturm-liouville problem

1. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem. x2y'' + xy' + λ y = 0, y(1) = 0, y(5) = 0. (b) Put the differential equation in self -adjoint form. (c) Give an orthogonality relation. 2. Hermite's differential equation y'' -2xy' + 2ny = , n =

Differential Equations and Green's Functions

Consider the inhomogeneous differential equation -u' + u = r(x) on (a,b) where r(x) is a continuous function on the interval (a,b) Find the solution to this differential equation in the form u = integral from a to b (G(x,s) r(s) ds) and determine G(x,s).

Graphing and Lagrange Multipliers

The plane, 4*x - 3*y + 8*z = 5, intersects the cone, z^2 = x^2 + y^2, in an ellipse. 1. Graph the cone, the plane and the ellipse 2. Using lagrange multipliers find the highest and lowest points on the ellipse. Please show grophs, equation of the ellipse and all work.

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

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/√(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

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

Existence and uniqueness theorem

The existence and uniqueness theorem for ordinary differential equations (ODE) says that the solution of a 1st order ODE with given initial value exists and is unique. It is discussed briefly on p. 528 of the text.<<< this just talks about the ability for a differential eqn. to have practical importance in predicting future valu

Stability properties of zero solution to a nonlinear system

Use the function V(x,y) = x^2 + y^2 to analyze the stability properties of the zero solution of the nonlinear system x' = x + 2xy^2 y' = - 2x^2y + y More specifically, what stability conclution(s) can be drawn? ( Justify your answer) Please I want a detailed and clear solution. Thanks.

Region R bounded by the given curves is revolved

(See attached file for full problem description) --- Find the volume of the solid generated when the region R bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps A sketch the region R B show a typical slice properly labeled C write a formula for the approximate vo

Minimum Material to Produce a Box

A company wishes to manufacture a box with a volume of 44 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material . Round to the nearest tenth , if necessary.

Newtons Method Using Mathematica 5

If its possible to answer these three questions using mathematica 5 if matlab looks similar, or the commands are similar then i guess matlab is fine... if its at all possible for mathetmatica it would be much appreciated Using Newtons Method 1. Plot f(x) = a on the interval - 3 &#8804; x &#8804; 3. a) Use Newton

Initial Conditions, Sources, Sinks, Nodes and Bifurcation

Our problem is to determine which values of D result in extinction and which result in survival. This can be done by studying equation (*), treating D as a bifurcation parameter see Section 2.6 a. Using technology to study solutions to an equation (*) for parameter values of 08, 0.7, 0,4, and 0.5. For each choice of D, use se

Propagated error

Find the propagated error for the area is the question: You must use differential to solve I cannot find the derivative of area of a triangle area = .5 b x h the base = 36cm height = 50cm and possible error for each is .25 cm

Temperature Change Differential Equations

A solid metal sphere at room temperature of 20 degrees Celsius is dropped into a container of boiling water (100 degrees Celsius). If the temperature of the sphere increases 2 degrees Celsius in 2 seconds, what will the temperature be at time t=6 seconds? how long will it take for the temperature of the sphere to reach 90 degree

Differential equations of Circles

Differential Equation (XV) Formation of Differential Equations by Elimination Find the differential equations of all circles of radius (whatever their radii or positions in the plane xOy).