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Supposed V(t) = 2cos(3t). If R = 4 and C = 0.5, use Eulers method to compute values of the solutions with the given inital conditions.
Model the data with two linear function. Let the independendt variable represent the number of years after 1960.
Prove that the spheres x2 + y2 +z2 = 16 and x2 + (y-5)2 + z2 = 9 intersect orthogonally.
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.
Find the volume of the solid generated when the region R bounded by the geven curves is revolved about the indicated axis.
Let A be any constant. Write down a differential equation satisfied by g(x)=f(A)f(x), and also give the value of g(0).
There is a type of differential equation which will always be solvable by two different methods.
For the following problems a function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one to one.
For the following graph the given functions on a computer screen, how are these graphs related?
X'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1 and identify critically damp, over-damped or under-damped (overdamped or underdamped)
A wholesaler that sells computer monitors finds that selling price “p” is related to demand “q” by the relation p=280 - .02q where p is measured in dollars.
Draw a graph that shows the path of the cat. Then write the geometric description of the path of the cat relative to the two trees.
What is trying to be solved is the proof in the first paragraph. All of the other information is there to help solve the problem.
Consider the differential equation (dy/dx) = (-xy^2)/2. Let y=f(x) be the particular solution to this differential equaiton with the initial condition f(-1)=2.
A corporation manufactures a product at two locations. The cost of producing x units at a location one and y unites at location two are C1(x)=.01x^2.
Let f(z) be an analytic function of the complex variable z on a domain D. Let C be a smooth closed curve inside D and suppose that C.
Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing.
Bayside General Hospital is trying to streamline its operations. A problem-solving group consisting of a nurse, a technician, a doctor, an administrator.
What is the value of y given by this particular solution when x=0.5 ? (give answer to 4 decimal places).
An open-top box is to be made as follows: squares of a certain size will be cut away from each of the four corners of a 20" x 30" rectangle.
The surrounding medium has a damping constant of 10 dyne*sec/cm. The mass is pushed 5 cm above its equilibrium position and released.
The equation f(x)= x^3 – 3x +1 has three distinct real roots. Approximate their locations by evaluating f at -2, -1, 0, 1, and 2.
Show that: lim (x+y)=o as x and y approach zero; using the epsilon-delta definition. Also, show that: lim f(x)=1 as x approaches zero; using the epsilon-delta.
Use implicit differentiation to find an equation of the line tangent to the curve x^3+2xy+y^3 = 13 at the point (1,2).
Using the method of undetermined coefficients to find the particular solution of the nonhomogeneous equation.