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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
With reference to Fig. 1(a) show that the magnification of an object is given by M=SID/SOD. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
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what is 36 percent as a fraction in simplest form
Julie had $500. She spent 20% of it on clothes and then 25% of the remaining money on CDs. How much money did Julie spend? Find out 20% of $500 by multiplying $500 by the decim
a) Specify that a tree has at least 2 vertices of degree 1. b) What is the largest number of vertices in a graph with 35 edges if all vertices are
THE MULTIPLICATION ALGORITHM : Some Class 3 children in a nearby school had been taught the standard multiplication. Algorithm, and had even done reasonably well in the tests bas
how to select out time for m2
sin 4 x - sin x = 0
Question 1. Use cylindrical coordinates to nd the mass of the solid of density e z which lies in the closed region Question 2. The density of a hemisphere of radius a (y
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