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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
What is a scatter diagram? A scatter diagram is a graphical representation of data points for a particular sample. Choosing a dissimilar sample or enlarging the original one ca
What is the Magna Carta
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
how to compare fractions
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
1 1 1 1 1 2 1 2 ? and 40/2=? 2/40=?
construct the green''s function that satisfies dG''''-(2x+1)G''+(x+1)G=delta(x-s), G(0,s)=G(1,s)=0
Consider the following two polynomials in F 17 [x] (a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials. (b) Use the FFT algorithm, by hand, to
Limits At Infinity, Part II : In this section we desire to take a look at some other kinds of functions that frequently show up in limits at infinity. The functions we'll be di
Given y = f(x) = x 2 + 2x +3 a) Use the definitional formula given below to find the derivative of the function. b) Find the value of the derivative at x = 3.
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