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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
Alexis needs to paint the four exterior walls of a large rectangular barn. the length of the barn is 80 feet the width is 50 feet and the height is 30 feet. The pain costs 28 dolla
Find the normalized differential equation which has {x, xex} as its fundamental set
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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
TRIGONOMETRY : "The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth." Example:
Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (
Arc Length with Polar Coordinates Here we need to move into the applications of integrals and how we do them in terms of polar coordinates. In this part we will look at the a
Polynomials in two variables Let's take a look at polynomials in two variables. Polynomials in two variables are algebraic expressions containing terms in the form ax n y m
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Kaylee makes 56 packages in seven hours Taylor makes 20% more packages in nine hours who makes more packages per hour
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