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Write the Taylor series with center zero for the function f(x) = In(1 + x2). Compute the first-order partial derivatives of f(x, y) = 2x/ x - y
Find the zero of the linear function f(x)=3x-12 , find the zeros and state the multiplicity of each.
A box with its base in the xy-plane has its four upper vertices on the surface with equation z = 48 - 3x^2 - 4y^2 . What is the maximum possible volume.
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.
How do you find the x, y, and z-intercepts of a 3-Dimensional graph step by step?
Last week's profits from a dry cleaners was $2000. Suppose the $2000 is invested at interest rate k, compounded continuously, and grows to $2983.65 in 5 years.
y’’ + k*y = 0 BC: y’(0) = 0 y’(L) = 0 Provide complete and step by step solution for the question and show calculations and use formulas.
Find the zeros and state the multiplicity of each for f(x)=x^2(x+3)(x+1)^4. Find the axis of symmetry of f(x)=x^2-2x+4
For the problem given below use the convolution theorem to write a formula for the solution of the I.V. problem in terms of f(t).
First find the general solution of the differential equation dy/dx = 3y. Then find the particular solution the satisfies the initial condition that y(1) = 4.
Use the method of Lagrange multipliers to find the extreme valus of 3x - 4y +12z on the spherical surface with equation x^2+y^2+z^2=1.
America creates more garbage than any other nation. According to Denis Hayes, president of Seattle’s nonprofit Bullitt Foundations and a founder of Earth Day.
Consider the limit state function L = X1 - X2. Compute the probability of failure Pf = P[L > 0]. Is your computed answer exact or approximate?
Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction.
Use Runge-Kutta method of order four to approximate the solution to the given initial value problem and compare the results to the actual values.
Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10.
A mass of clay of volume 432 in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?
Let g(v) be the distance the same car goes on one liter of gas at velocity v. what is the relationship between f(v) and g(v) ? find g(80) and g1(80).
Find the relative maxima, relative minima, and saddle points of the function (x^2)*y - 6*(y^2) - 3*(x^2).
A company paid off a $10,000 long-term note by issuing common stock to the creditor. This transaction would be reflected on the company's statement of cash flow
What value of t will maximize the government's tax revenue? What is the government's maximum tax revenue?
Find the differential equation that governs the position of the body over time relative to the equilibrium position of the spring.
Substitution Methods and Exact Equations. Verify that the given differential equation is exact; then solve it.
Show that the substitution v = lny transforms the differential equation dy/dx + P(x)y = Q(x)(ylny) into the linear equation dv/dx + P(x) = Q(x)v(x)
Show that the one parameter family of straight lines described by y(x) = Cx + g(C) is a general solution of y = xy' + g(y').