Calculus Answers

form the PDE
2z=(ax+y)^2 + b

Write the equation of a line in point slope form that passes through g(-2) and g(3) when
g(x)=-x^2+3

intregation of p.dv=? (upper limit v_2 and lower limit v_1)

Find the values of x for which the function
( ) 2 1
2
f x = x − x +
is increasing or decreasing. Sketch the graph of y = f (x)

let A=X2YZI-2XZ3J-XZ2 and B =4zi+yj+4x2k find a2/axay at (1,0,-2)

Intravenous infusion of glucose into the blood-stream of a patient is an important medical technique. To study this process, let G(t) be the amount of glucose in the patient’s blood stream t minutes after the process begins. Assume that glucose is infused into the bloodstream at a constant rate of k(in g/min). Also assume that at the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of glucose still present, with the proportionality constant r.(a) Write a first-order differential equation describing this process that should be satisfied by G(t).(b) Suppose that glucose is not present initially in the patient’s bloodstream; solve the differential equation in (a) above which satisfies the initial condition G(0) = 0.
(c) Find
lim t→∞G(t).

Find the area enclosed by the curve r = a(1-cos theta).

Intravenous infusion of glucose into the blood-stream of a patient is an important medical technique. To study this process, let G(t) be the amount of glucose in the patient’s blood stream t minutes after the process begins. Assume that glucose is infused into the bloodstream at a constant rate of k(in g/min). Also assume that at the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of glucose still present, with the proportionality constant r.

A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 260 m and the minimum diameter, 500 m above the base, is 200 m. Find an equation for the tower. (Assume the position of the hyperboloid is such that the center is at the origin with its axis along the z-axis, and the minimum diameter at the center.)