Explore BrainMass

Explore BrainMass

    Calculus and Analysis

    BrainMass Solutions Available for Instant Download

    Find the Change in Revenue

    Find the change in Revenue, R. In each case, that the number of units, x, increases by three from the specified value of x. dR/dx = 75 (20 + 900/x), x = 500.

    Elimination and differential equation

    Please help on these section 5.2 # 4,8 see attached Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t.

    Solving Several Differential Equations

    Please help solving these problems section 4.7 # 4,6,12 section 4.8 # 2,6,8,12 section 4.9 #4,8,12 See attached Find a general solution to the given Cauchy-Euler equation... Using the paradigm, what are the inertia, dampness, and stiffness.... Use the energy integral lemma.... Use reduction of order to solve....

    Radius of Convergence

    There's three questions for this problem. Please show all work. Thanks!!! Find the radius of convergence for each of the following. Give reasons for your answers. (see attached)

    Differential equation and convergence

    See attached. Please show all the work. Thanks! Suppose converges for all x in Real Number to a solution to the differential equation a) Find a relationship among and for ? b) Compute ?

    Volume of Revolution Problem

    Find the volume of the solid of revolution formed by rotating about the x-axis the finite region in Quadrant I bounded by the graphs of y=xcos(pi*x^3/2) and y=sqrt(1-x^6) and the y-axis. A. 9p/11 B. 9p/17 C.11p/17 D.11p/42 E.29p/42

    Example Characteristic Equation

    See attached for equation. Write the characteristic equation for the linear homogeneous differential equation. Solve the characteristic equation, and write the general solution.

    Characteristic Equations: Example Problems

    Please show all steps to solution. See attached for equations. Write the characteristic equation for the linear homogeneous differential equation. Solve the characteristic equation, and write the general solution.

    (1) Find a general solution to the following non homogeneous differential equation: y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2 (2) Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equations (a) y'' - y' + y = (e^t + t)^2 (b) y'' + y' + y = e^t + 7 (c) y'' - 2y' + 3y = cosh t (3) Find general solution to the following differential equations: y'' + 4y = sin q - cos q y'' + y' - 12 y = e^t + e2t - 1 y'' - 4y' + 4y = t^2 e^t - e^(2t) (4) Find a particular solution to the given higher order differential equation: y^(4) - 5y'' + 4y = 10 cos t - 20 sin t

    Please help working on these attached problems section 4.5 #6,10,12,14,20,28,36,38 Thanks (6) Find a general solution to the following non homogeneous differential equation: y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2 Decide whether the method of undetermined coefficients together with superposition

    Differential Equations Examples for an Initial Value Problem

    Hi, Please help solving these problems section 4.3 # 4,16,22,34,38 See attached The auxiliary equation for the given differential equation has complex roots. Find a general solution. Solve the given initial value problem. Prove the sum of angle formula for the sine function by following these steps.

    Nonhomogeneous equation

    Please show all working for solution. Use the variation of parameters to find a particular solution to the nonhomogeneous equation y''+y=secx Write out the general solution.

    Extreme values

    1.)f(x,y)= 5 - 3x + 4y, D is the closed triangular region with vertices (0,0), (4,0), and (4,5) 2.)f(x,y)= x^2 + 2xy + 3y^2, D is the closed triangular region with vertices (-1,1), (2,1), and (-1,-2) 3.)f(x,y)= 1 + xy - x - y, D is the region bounded by the parabola y=x^2 and the line y=4

    optimal coughing radius

    When a foreign object gets stuck in your windpipe you cough. The radius of your windpipe contracts so as to increase the air velocity and dislodge the obstruction. It can be shown that air velocity is related to windpipe radius by v(r) = (r0 - r)r^2 ,where r0 is the usual 'rest radius' of the windpipe. Physical constraints preve

    Deriving the volume element in spherical coordinates

    A differential of volume is given by: dV = r^2*sin(theta)*dr*d(theta)*d(phi) can you derive this for me i.e. using a differential of volume and spherical coordinates show how this equation is arrived at? r is a radius, theta is the angle in the x-y plane and psi is the the z-y plane Please show a diagram

    Linear Approximations and Differentials

    2.8 Exercises Find the linearization L(x) of the function at a. 2. f(x) = 1/sqrt(2 + x), a = 0 Explain, in terms of linear approximations or differentials, why the approximation is reasonable. 16. (1.01)^6 ~ 1.06 24. Use differentials to estimate the amount of paint needed to apply a coat of pain 0.05 cm thick to

    Solving Limits Algebraically

    I came across the following limit while studying and I'm having trouble doing this algebraically. Please help. lim (3sin4x/sin3x) x->0.

    Gradient and Rate of Change

    Find the gradient of f Evaluate the gradient at the point P Find the rate of change of f at P in the direction of the vector u f(x,y,z)= xy^2z^3, P(1,-2,1), u=<1/squareroot(3), -1/squareroot(3), 1/squareroot(3)>.

    Volume and Parametric Curves

    See attached let W be the region consisting of all the points (x, y) such that -1<=x<=1 and 4/(5+2x+x^2)<=y<=1. Compute the volume of the solid generated when W is rotated about the line y=1. Calculus with parametric curves

    Quasilinear equation

    I have to solve the following quasilinear equation using the method of characteristics: xu_x + yu_y = xy u|y=x^2 = sinx dx/dt = x gives me lnx = t +c_1 dy/dt= y gives me lny = t + c_2 But what do I do with du/dt = xy - yu? Thank you.

    Differentiable Vector Functions

    Please see the attached document regarding homework specifics. Thank-you for your help. I have attached both versions of Microsoft Word (just in case). Let f: &#8477;3 &#8594; &#8477; be differentiable. Making the substitution x = &#961; cos(&#952;) sin(&#966;), y = &#961; sin(&#952;) sin(&#966;), z = &#961; cos(&#966;)