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Calculus and Analysis

Friction and Equations of Motion

A particle of mass m moves under the influence of constant force f and the friction force γ(xdot)n Its equation of motion reads: m(x-double dot) + γ(xdot)n = f Find x(t) for n=1 and n=2 if x=0 and x-dot=0 at t=0 Check that your solutions exhibit the correct behavior in the limit. Please see the attac

High School Calculus Problems

4. Find the center, vertices and foci of 4x^2 + 9y^2 -8x +36y +4 =0. Graph, labeling all relevant points including the foci. 5. Find the equation of the hyperbola whose center is the origin, vertex at (2,0) and focus at (3,0). Write the equation of the asymptotes. 6. Find the center, vertices, foci and asymptotes

Domain, range, intercepts

F(x,y)=1/(x^2+y^2) Is the domain (-infinity, 0) union (0, infinity)? Is the range (0, 1]? What are the x and y intercepts and is the z intercept undefined?

Finding X, Y and Z Intercepts of 3-D Graphs

How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step? I am trying to interpret some graphs and would like this information to assist me in the interpretation. keywords: 3D, 3Dimensional

Simple harmonic oscillation driven by an external force

2. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t. 10. As in Exercise 9, consider a spring with mass m, spring constant k,

Finding the Equation of a Tangent Line

Let h(t) = ln(t) +1. Determine the equation of the line that is tangent to the graph of h(t) at the point where t =3. Provide a graph of your work showing the function and the tangent line you are identifying. (Note: You may round all decimal values in this problem to the nearest thousandth.)

LaPlace Transforms and Differential Equations : Masses and Springs

In system below spring k1 is anchored at the left side and has a spring constant of k1, spring K2 has a spring constant of k2; the system is not subjected to friction or damping. Block M is subjected to a periodic driving force f(t) = A sin(ωt). Both masses are initially at rest in the equilibrium position Using L

LaPlace Transforms and Differential Equations : Masses and Springs

Two objects of mass M1 and M2 are attached to the opposite ends of a spring having a spring constant K; the entire apparatus is placed on a frictionless table. The spring is stretched and then released. Using Laplace transforms to solve the differential equations show that the period is: See attached file for full problem des

Inverse LaPlace Transform two different ways

Find the Inverse LaPlace Transform using different methods described in the attachment. To see the description of the problem in its true format, please download the attached question file.


1) The terms of series are defined recursively by the equations: a1=2 a(n+1)=(5n+1)/(4n+3)an Determine whether ?" an converges or diverges 2) a) Show that ?" (from n=0 to infinity) [x^n/n!]converges for all x b) Deduce that lim ( n--> infinity)[x^n/n!] = 0 for all x

Applications of Cost Functions

4. A hospital has seven large identical heat pumps. If one of the heat pumps malfunctions, it could seriously impact hospital operations. If preventive maintenance is performed weekly, it costs $1200 to perform preventive maintenance (PM) on all seven of them. If one of the heat pumps breaks down between PM inspections, the av

Solving Differential Equations, Volumes of Solids and Taylor Series

See attached file for full problem description. 1. First find a general solution of the differential equation dy 3y dx = . Then find a particular solution that satisfies the initial condition that y(1) = 4. 2. Solve the initial value problem dy y3 dx = , y(0) = 1. 3. Nyobia had a population of 3 million in 1985. Assum

Initial Value Problems, Differential Equations and Springs

1. Solve the initial-value problems and graph the solutions on the same set of axes. y'' + 4y' + 2y = 0 y(0) = 5; y'(0) = 0 y'' + 4y' + 2y = 0 y(0) = 0; y'(0) = 5 2. Repeat problem 1 for the equation: y'' + 2y' + 5y = 0 y(0) = 5; y'(0) = 0 y'' + 2y' + 5y = 0 y(0) = 0; y'(0) = 5

Solving Inequalities, Limits and Derivatives (18 Problems)

Please see the attached file for the fully formatted problems. Includes: Solve the following inequalities/equations expressing the solution. Show all work and box the final answer. Write an equation for the line described below. Graph the following function. What symmetries, if any, does the graph have? Find the v

Continuously Compounding Interest

Susie is opening an online savings account with an interest rate of 5.5%, compounded continuously. She wants the account to have a balance of $4,000 after 6 years. Assuming the interest rate stays the same, how much money must Susie deposit now in order to reach her goal? (Show formula and answer in a complete sentence)