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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
Each Child Is Unique : Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth
Let {An} be sequence of real numbers. Define a set S by: S={i ? N : for all j > i, ai
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Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0 y′ (0)=-7 Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0
Which of those territories never was a Venitian possesion? Cyprus Morea Crete Sicily
Area between Curves In this section we will be finding the area between two curves. There are in fact two cases that we are going to be looking at. In the first case we des
Factoring By Grouping It is a method that isn't utilized all that frequently, but while it can be used it can be somewhat useful. Factoring by grouping can be nice, however it
The diagram below shows the cross section of a pipe 1/2 inch thick that has an inside diameter of 3 inches. Determine the area of the shaded region in terms of π. a. 8.75π i
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
Tom is cutting a piece of wood to form a shelf. He cut the wood to 3.5 feet, but it is too long to fit in the bookshelf he is forming. He decides to cut 0.25 feet off the board. Ho
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