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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.
Use the differential equation for y (not the solution formula) to show that the quantity Q also undergoes exponential decay with rate constant k.
Find the length of the graph of y = 1/3 x3/2 - x1/2 from (1, - 2/3) to (4, 2/3).
Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = v(3x+ x2)
Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt.
Find the present value and future value of an income stream of $1000 a year, for a period of 5 years, if the interest rate is 8%.
Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.
What dimensions will maximize the enclosed area? Be sure to verify that you have found the maximum enclosed area.
An object having a mass of 1 kg. is suspended from a spring with a spring constant (k) of 24 Newtons/meter.
Suppose that the cost of preventive maintenance increases as the weeks between the preventive maintenance increases.
The second way, find the inverse LaPlace transform of 1 / s2 using the integration theorem, and then apply the s-shift theorem.
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).