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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
tan 2x = 1
Evaluate subsequent proportion: Example 2: If 5 pounds of apples cost 80 cents, how much will 7 pounds cost? Solution: By using x for the cost of 7 pounds of appl
The sum of -4 and a number is equal to -48. What is the number? Let x = the number. Because sum is a key word for addition, the equation is -4 + x = -48. Add 4 to both sides o
what is the difference between North America''s part of the total population and Africa''s part
To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.
Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
Evaluating a Function You evaluate a function by "plugging in a number". For example, to evaluate the function f(x) = 3x 2 + x -5 at x = 10, you plug in a 10 everywhere you
If a tabletop has a diameter of 42 in, Detremine the surface area to the nearest inch? (π = 3.14) a. 1,384 in 2 b. 1,319 in 2 c. 1,385 in 2 d. 5,539 in 2 c. Th
8+2=
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