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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
Max can paint a house in 3 hours. Saria can paint a house in 5 hours. working together, how long will it take both Saria and Max to paint a house?
A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro
Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of
On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +
Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2, Subject to the constraints: X1+ X2 = 4 X1+ X2 = 2 X1, X2 = 0
inverse rule of x3-5
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